Exhibit 10.2

PARENT LOCK-UP AND SUPPORT AGREEMENT

PARENT LOCK-UP AND SUPPORT AGREEMENT (this “Agreement”) is made and entered into as of January 21, 2026, by and among Hecate Energy Group, LLC, a Delaware limited liability company (the “Company”), EGH Acquisition Corp., a Cayman Islands exempted company (“SPAC”), and Hecate Holdings LLC, a Delaware limited liability company (“Parent”).

WHEREAS, capitalized terms used but not otherwise defined in this Agreement shall have the meanings ascribed thereto in the Business Combination Agreement, by and among the Company, the SPAC and Parent dated as of January 21, 2026 (as further amended or modified in whole or in part from time to time in accordance with such agreement, the “Combination Agreement”);

WHEREAS, Parent is, as of the date of this Agreement, the sole legal owner of 100% of the Company Interests (collectively, “Company Interests”) (or any securities convertible into or exercisable or exchangeable for Company Interests) acquired by Parent after the date of this Agreement and prior to the Closing, being collectively referred to herein as the “Subject Interests”); and

WHEREAS, as a condition to their willingness to enter into the Business Combination Agreement, the Company and SPAC have requested that Parent enter into this Agreement.

NOW, THEREFORE, the parties hereto agree as follows:

ARTICLE I
Representations and Warranties of Parent

Parent hereby represents and warrants to the Company and SPAC as follows:

1.1 Corporate Organization. Parent has been duly organized and is validly existing and in good standing under the Laws of the state of Delaware and has the requisite power and authority to own, lease and operate its assets and properties and to conduct its business as it is now being conducted. Parent is duly licensed or qualified and in good standing (where such concept is applicable) as a foreign entity in each jurisdiction in which the ownership of its property or the character of its activities is such as to require it to be so licensed or qualified.

1.2 Due Authorization. Parent has all requisite corporate power and authority to execute and deliver this Agreement and each other Transaction Document to which it is or will be a party and to perform its obligations hereunder and thereunder and to consummate the Business Combination. The execution, delivery and performance of this Agreement and such other Transaction Documents and the consummation of the Business Combination have been duly and validly authorized and no other corporate proceeding on the part of Parent is necessary to authorize this Agreement or any other Transaction Documents or Parent’s performance hereunder or thereunder. This Agreement has been, and each such other Transaction Document has been or will be (when executed and delivered by Parent), duly and validly executed and delivered by Parent and, assuming due and valid authorization, execution and delivery by each other party hereto and thereto, this Agreement constitutes, and each such other Transaction Document constitutes or will constitute, a valid and binding obligation of Parent, enforceable against Parent in accordance with its terms, subject to the Remedies Exceptions.

1.3 Governmental Approvals. No notice to, action by, consent, approval, permit or authorization of, or designation, declaration or filing with, any Governmental Authority is required on the part of Parent with respect to Parent’s execution, delivery and performance of this Agreement and the other Transaction Documents to which it is or will be a party and the consummation of the Business Combination, except for (a) applicable requirements, if any, of the Securities Act, the Exchange Act, and/or any state “blue sky” securities Laws, and the rules and regulations thereunder and (b) where the failure to obtain or make such consents or to make such filings or notifications would not prevent, impede or, in any material respect, delay or adversely affect the performance by Parent of its obligations under this Agreement.

1.4 No Conflict. The execution, delivery and performance of this Agreement and any other Transaction Document to which Parent is or will be a party, and the consummation of the Business Combination do not and will not (a) conflict with or violate any provision of, or result in the breach of Parent’s Organizational Documents, (b) contravene or conflict with or constitute a violation of any provision of any Law, permit or governmental order binding on or applicable to Parent, (c) violate, conflict with, result in a breach of any provision of or the loss of any benefit under, constitute a default under, give rise to any obligation to make payments or provide compensation under, result in the termination or acceleration of, a right of termination, cancellation, modification, or acceleration or amendment under, accelerate the performance required by, any of the terms, conditions or provisions of any contract to which Parent is a party, (d) result in the creation of any Lien upon any of the properties or assets of Parent, (e) give rise to any obligation to obtain any third party consent or to provide any notice to any Person under any contract to which Parent is a party or (f) give any Person the right to declare a default, exercise any remedy or claim, or cancel, terminate or modify any right, benefit, obligation or other term under, any of the terms, conditions or provisions for any contract to which Parent is a party, except, in the case of each of clauses (b) through (f), that would not prevent, impede or, in any material respect, delay or adversely affect the performance by Parent of its obligations under this Agreement.

1.5 Subject Interests. Parent is the sole legal owner of the Subject Interests, and all such Subject Interests are owned by Parent free and clear of all liens or encumbrances, other than liens or encumbrances pursuant to this Agreement, Company LLC Agreement, the Business Combination Agreement or applicable federal or state securities laws. Parent does not legally own any shares of Company other than the Subject Interests. Parent has the sole right to vote the Subject Interests, and none of the Subject Interests is subject to any voting trust or other agreement, arrangement or restriction with respect to the voting of the Subject Interests, except as contemplated by this Agreement, the Business Combination Agreement or the Company LLC Agreement.

1.6 Business Combination Agreement. Parent understands and acknowledges that the Company and SPAC are entering into the Business Combination Agreement in reliance upon Parent’s execution and delivery of this Agreement. Parent has received a copy of the Business Combination Agreement and is familiar with the provisions of the Business Combination Agreement.

ARTICLE II
Representations and Warranties of SPAC

SPAC hereby represents and warrants to Parent and the Company as follows:

2.1 Corporate Organization. SPAC is an exempted company duly incorporated, is validly existing and is in good standing under, the Laws of the Cayman Islands and has the requisite corporate power and authority to own, lease and operate its assets and properties and to conduct its business as it is now being conducted. SPAC is duly licensed or qualified and in good standing (where such concept is applicable) as a foreign entity in each jurisdiction in which the ownership of its property or the character of its activities is such as to require it to be so licensed or qualified.

2.2 Due Authorization. SPAC has all requisite corporate power and authority to execute and deliver this Agreement and each other Transaction Document to which it is or will be a party and (subject to the consents, approvals, authorizations and other requirements described in the Business Combination Agreement and obtaining the Shareholder Approval) to perform its obligations hereunder and thereunder and to consummate the Business Combination. The execution, delivery and performance of this Agreement and such other Transaction Documents and the consummation of the Business Combination have been duly authorized by the SPAC Board and, other than the consents, approvals, authorizations and other requirements described in the Business Combination Agreement and obtaining the Shareholder Approval, no other corporate proceeding on the part of SPAC is necessary to authorize this Agreement or any other Transaction Documents or SPAC’s performance hereunder or thereunder. This Agreement has been, and each such other Transaction Document has been or will be (when executed and delivered by SPAC), duly and validly executed and delivered by SPAC and, assuming due and valid authorization, execution and delivery by each other party hereto and thereto, this Agreement constitutes, and each such other Transaction Document constitutes or will constitute, a valid and binding obligation of SPAC, enforceable against SPAC in accordance with its terms, subject to the Remedies Exceptions.

2.3 No Conflict. Subject to the receipt of the consents, approvals, authorizations and other requirements set forth in the Business Combination Agreement and obtaining the Shareholder Approval, the execution, delivery and performance of this Agreement and any other Transaction Document to which SPAC is or will be a party, and the consummation of the Business Combination does not and will not (a) conflict with or violate any provision of, or result in the breach of SPAC’s Organizational Documents, (b) contravene or conflict with or constitute a violation of any provision of any Law, permit or governmental order binding on or applicable to SPAC, (c) violate, conflict with, result in a breach of any provision of or the loss of any benefit under, constitute a default under, give rise to any obligation to make payments or provide compensation under, result in the termination or acceleration of, a right of termination, cancellation, modification, or acceleration or amendment under, accelerate the performance required by, any of the terms, conditions or provisions of any contract to which SPAC is a party, (d) result in the creation of any Lien upon any of the properties or assets of SPAC (including the Trust Account), (e) give rise to any obligation to obtain any third party consent or to provide any notice to any Person under any contract to which SPAC is a party or (f) give any Person the right to declare a default, exercise any remedy or claim, or cancel, terminate or modify any right, benefit, obligation or other term under, any of the terms, conditions or provisions for any contract to which SPAC is a party, except, in the case of each of clauses (b) through (f), that would not prevent, impede or, in any material respect, delay or adversely affect the performance by SPAC of its obligations under this Agreement.

ARTICLE III
Representations and Warranties of the Company

The Company hereby represents and warrants to Parent and SPAC as follows:

3.1 Corporate Organization. The Company has been duly organized and is validly existing and in good standing under the Laws of the state of Delaware and has the requisite power and authority to own, lease and operate its assets and properties and to conduct its business as it is now being conducted. The Company is duly licensed or qualified and in good standing (where such concept is applicable) as a foreign entity in each jurisdiction in which the ownership of its property or the character of its activities is such as to require it to be so licensed or qualified.

3.2 Due Authorization. The Company has the requisite corporate power and authority to execute and deliver this Agreement and each other Transaction Document to which it will be a party and (subject to the consents, approvals, authorizations and other requirements described in the Business Combination Agreement) to perform all obligations to be performed by it hereunder and thereunder and to consummate the Business Combination. The execution, delivery and performance of this Agreement and such other Transaction Documents and the consummation of the Business Combination have been duly authorized by the Company Board and, other than the consents, approvals, authorizations and other requirements described in the Business Combination Agreement, no other corporate proceeding on the part of the Company is necessary to authorize this Agreement or any other Transaction Documents or the Company’s performance hereunder or thereunder. This Agreement has been, and each such other Transaction Document has been or will be (when executed and delivered by Company), duly and validly executed and delivered by the Company and, assuming due and valid authorization, execution and delivery by each other party hereto and thereto, this Agreement constitutes, and each such other Transaction Document constitutes and will constitute, a valid and binding obligation of the Company, in accordance with its terms, subject to the Remedies Exceptions.

3.3 No Conflict. Subject to the receipt of the consents, approvals, authorizations and other requirements set forth in the Business Combination Agreement, the execution, delivery and performance by the Company of this Agreement and the other Transaction Documents to which it is or will be a party and the consummation by the Company of the Business Combination do not and will not (a) contravene, breach or conflict with the Organizational Documents of the Company, (b) contravene or conflict with or constitute a violation of any provision of any Law, permit or governmental order binding upon or applicable to the Company or any of its assets or properties, or (c) violate, conflict with, result in a breach of any provision of or the loss of any benefit under, constitute a default under, give rise to any obligation to make payments or provide compensation under, result in the termination or acceleration of, result in a right of termination, cancellation, modification, acceleration or amendment under, or accelerate the performance required by, any of the terms, conditions or provisions of any contract, (d) result in the creation or imposition of any Lien on any asset or property of the Company (other than Permitted Liens) or on any equity security of the Company (other than any Liens arising under applicable Securities Laws), (e) give rise to any obligation to obtain any third party consent or to provide any notice to any Person or (f) give any Person the right to declare a default, exercise any remedy, claim, rebate, chargeback, penalty or change in delivery schedules, accelerate the maturity or performance of or cancel, terminate or modify any right, benefit, obligation or other term under, any of the terms, conditions or provisions for any contract to which the Company is a party, except, in the case of each of clauses (b) through (f), that would not prevent, impede or, in any material respect, delay or adversely affect the performance by the Company of its obligations under this Agreement.

ARTICLE IV
Certain Covenants of Parent

Parent covenants and agrees during the period starting from the date hereof until the earlier of (1) the Closing and (2) the termination of the Business Combination Agreement in accordance with its terms (the “Exclusivity Period”) as follows:

4.1 No Transfer. During the Exclusivity Period, other than (x) pursuant to this Agreement; (y) upon the consent of the Company and SPAC, or (z) pursuant to a Permitted Transfer, Parent shall not, directly or indirectly,

(a) (i) sell, offer to sell, contract or agree to sell, hypothecate, pledge, grant any option to purchase or otherwise dispose of, or agree to dispose of, directly or indirectly, or establish or increase a put equivalent position or liquidate or decrease a call equivalent position within the meaning of Section 16 of the Exchange Act, and the rules and regulations of the SEC promulgated thereunder, any Subject Interest, (ii) enter into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of any Subject Interests, whether any such transaction is to be settled by delivery of such securities, in cash or otherwise, or (iii) publicly announce any intention to effect any transaction specified in clause (i) or (ii) (the actions specified in clauses (i)-(iii), collectively, “Transfer”), other than pursuant to the Business Combination,

(b) grant any proxies or powers of attorney or enter into any voting arrangement, whether by proxy, voting agreement, voting trust, voting deed or otherwise (including pursuant to any loan of Subject Interests), or enter into any other agreement, with respect to any Subject Interests, in each case, other than as set forth in this Agreement, the Business Combination Agreement or any other Transaction Documents,

(c) take any action that would reasonably be expected to make any representation or warranty of Parent herein untrue or incorrect, or would reasonably be expected to have the effect of preventing or disabling Parent from performing its obligations hereunder, or

(d) commit or agree to take any of the foregoing actions.

As used herein, “Permitted Transfer” means any of the following, provided that the recipient of a Permitted Transfer must enter into a written agreement, in substantially the form of this Agreement, agreeing to be bound by the obligations of the Parent with respect to such shares under this Agreement, including the provisions of Sections 4.1 and 5.1:

Any action attempted to be taken in violation of this Section 4.1 will be null and void. Parent agrees with, and covenants to, the Company and SPAC that, except pursuant to a Permitted Transfer, Parent shall not request that the Company register the Transfer (by book-entry or otherwise) of any certificated or uncertificated interest representing any of the Subject Interests.

4.2 New Shares. In the event that prior to the Closing (a) any Company Interests or other shares of the Company are issued or otherwise distributed to Parent pursuant to any stock dividend or distribution, or any change in any of the Company Interests or other share capital of the Company by reason of any stock split-up, recapitalization, combination, exchange of shares or the like, (b) Parent acquires legal or beneficial ownership of any Company Interests after the date of this Agreement, including upon exercise of options, settlement of restricted share units or capitalization of working capital loans or (c) Parent acquires the right to vote or share in the voting of any Company Interests or other shares of the Company after the date of this Agreement (collectively, the “New Securities”), the term “Subject Interests” shall be deemed to refer to and include such New Securities (including all such stock dividends and distributions and any securities into which or for which any or all of the Subject Interests may be changed or exchanged into).

4.3 Additional Matters. Parent shall, from time to time, (a) execute and deliver, or cause to be executed and delivered, such additional or further consents, documents and other instruments as the Company or SPAC may reasonably request for the purpose of effectively carrying out the transactions contemplated by this Agreement, the Business Combination Agreement and the other Transaction Documents and (b) refrain from exercising any veto right, consent right or similar right which would prevent, impede or, in any material respect, delay or adversely affect the consummation of the Business Combination.

4.4 Consent to Disclosure. Parent consents to and authorizes the Company or SPAC, as applicable, to publish and disclose in all documents and schedules filed with the SEC or any other Governmental Authority or applicable securities exchange, and any press release or other disclosure document that the Company or SPAC, as applicable, reasonably determines to be necessary or advisable in connection with the Business Combination or any other transactions contemplated by the Business Combination Agreement or this Agreement, Parent’s identity and ownership of the Subject Interests, the existence of this Agreement and the nature of Parent’s commitments and obligations under this Agreement, and Parent acknowledges that the Company or SPAC may, in their sole discretion, file this Agreement or a form hereof with the SEC or any other Governmental Authority or securities exchange. Parent agrees to promptly give the Company or SPAC, as applicable, any information that is in its possession that the Company or SPAC, as applicable, may reasonably request for the preparation of any such disclosure documents, and Parent agrees to promptly notify the Company and SPAC of any required corrections with respect to any written information supplied by it specifically for use in any such disclosure document, if and to the extent that Parent shall become aware that any such information shall have become false or misleading in any material respect.

ARTICLE V
Other Agreements

5.1 Lock-Up Provisions.

(a)  Subject to the exceptions set forth herein, from the Closing until the date that is one year after Closing Date (the “Lock-Up Period”), Parent agrees not to, without the prior written consent of the SPAC Board, Transfer any Company Units or SPAC Class V Common Stock (or any SPAC Class A Common Stock issued in exchange for Company Units and SPAC Class V Common Stock) issued to Parent pursuant to the Business Combination upon the execution of the Company A&R LLC Agreement (the “Locked-Up Shares”); provided, however, (x) from and after the date that is six months after the Closing, Parent may Transfer up to 10% of the Locked-Up Shares; (y) from and after the date that is nine months after the Closing, Parent may Transfer up to an additional 5% of the Locked-Up Shares; and (z) if any other holder of securities of the SPAC enters into an agreement relating to the subject matter set forth in this Section 5.1 in connection with the Closing on terms and conditions that are less restrictive than those agreed to herein (or such terms and conditions are subsequently relaxed including as a result of a modification, waiver or amendment), then the less restrictive terms and conditions shall apply to Parent or any permitted transferee (or any subsequent permitted transferee).

(b)  The restrictions set forth in Section 5.1(a) (the “Lock-Up Restrictions”) shall not apply to:

(i) in the case of an individual, Transfers as a gift to such person’s immediate family or to a trust, the beneficiary of which is a member of such person’s immediate family, an affiliate of such person or to a charitable organization;

(ii) in the case of an individual, Transfers by virtue of laws of descent and distribution upon death of such person;

(iii) in the case of an individual, Transfers pursuant to a qualified domestic relations order;

(iv) pro rata distributions from the Parent to its respective members, partners or shareholders pursuant to the Parent’s limited liability company agreement or other charter documents;

(v) by virtue of the laws of Delaware or the Parent’s limited liability company agreement upon dissolution of the Parent,

(vi) in the event that, subsequent to the consummation of a Business Combination, the SPAC completes a liquidation, merger, share exchange or other similar transaction which results in all of its shareholders having the right to exchange their Class A Common Stock for cash, securities or other property,

(vii) to a nominee or custodian of a person or entity to whom a transfer would be permissible under clauses (i) through (vii),

(viii)  pledges of any Locked-Up Shares to a financial institution that create a pledge, hypothecation or security interest in such Locked-Up Shares pursuant to a bona fide loan or indebtedness transaction so long as Parent continues to control the exercise of the voting rights of such pledged Locked-Up Shares, and any foreclosures on such pledged Locked-Up Shares,

(ix)  Transfers to any creditors of Parent or the Company in settlement of indebtedness owed by Parent, the Company or its subsidiaries to such creditors;

(x)  the establishment of a trading plan that meets the requirements of Rule 10b5-1(c) under the Exchange Act (a “Trading Plan”); provided, however, that no sales of Locked-Up Shares shall be made by Parent pursuant to such Trading Plan during the Lock-Up period and no public announcement or filing is voluntarily made regarding such plan during the Lock-Up Period; and

(xi)  transactions to satisfy any U.S. federal, state, or local income tax obligations of Parent (or its direct or indirect owners) arising from a change in the U.S. Internal Revenue Code of 1986, as amended (the “Code”), or the U.S. Treasury Regulations promulgated thereunder (the “Regulations”) after the date on which the Business Combination Agreement was executed by the parties, and such change prevents the Business Combination from qualifying as a “reorganization” pursuant to Section 368(a) of the Code (and the Business Combination do not qualify for similar tax-free treatment pursuant to any successor or other provision of the Code or Regulations taking into account such changes), in each case, solely to the extent necessary to cover any tax liability as a result of the transaction.

provided, however, that in the case of clauses (i) through (v), (vii), (viii) and (ix) these permitted transferees must enter into a written agreement, in substantially the form of this Agreement, agreeing to be bound by the Lock-Up Restrictions and shall have the same rights and benefits under this Agreement; provided further however, that in the case of a Transfer pursuant to clause (iv) above to any member of Parent owning as of the date of this Agreement an equity interest in Parent of 1% or less, Parent may in its discretion make such Transfer without requiring the transferee to agree to be bound by the Lock-Up Restrictions, so long as the transferee agrees with the Company to be bound by the Company’s insider trading policy and resulting black-out periods. For purposes of this paragraph, “immediate family” shall mean a spouse, domestic partner, child, grandchild or other lineal descendant (including by adoption), father, mother, brother or sister of an individual; and “affiliate” shall have the meaning set forth in Rule 405 under the Securities Act of 1933, as amended.

(c)  For the avoidance of doubt, Parent shall retain all of its rights as a shareholder of the Company during the Lock-Up Period with respect to Locked-Up Shares it owns, including the right to receive dividends with respect thereto and to vote any Locked-Up Shares.

(d)  In furtherance of the foregoing, the Company, and any duly appointed transfer agent for the registration or transfer of the Locked-Up Shares, are hereby authorized to decline to make any transfer of securities if such Transfer would constitute a violation or breach of the Lock-Up Restrictions.

ARTICLE VI
General Provisions.

6.1 Notice. All notices, requests, claims, demands and other communications hereunder shall be in writing and shall be given (and shall be deemed to have been duly given upon receipt) by delivery in person, by email or by registered or certified mail (postage prepaid, return receipt requested) to the Company and SPAC in accordance with Section 11.02 of the Business Combination Agreement (or at such other address for a party as shall be specified by like notice)

6.2 Governing Law. This Agreement, and all Actions or causes of action based upon, arising out of, or related to this Agreement or the transactions contemplated hereby, shall be governed by, and construed in accordance with, the internal substantive Laws of the State of New York applicable to contracts entered into and to be performed solely within such state, without regard to its conflict of laws provisions.

6.3 Miscellaneous. The provisions of Article XI (other than Section 11.06) of the Business Combination Agreement are incorporated herein by reference, mutatis mutandis, as if set forth in full herein.

6.4 Legends. The Company shall remove, and shall cause to be removed (including by causing its transfer agent and The Depository Trust Company (as applicable) to remove), any legends, marks, stop-transfer instructions or other similar notations pertaining to the lock-up arrangements herein from the book-entries evidencing any Locked-Up Shares at the time any such share is no longer subject to the Lock-Up Restrictions. Any holder of a Locked-Up Share is an express third-party beneficiary of this Section 6.4 and entitled to enforce specifically the obligations of the Company set forth in this Section 6.4 directly against the Company.

6.5 Termination. This Agreement shall be effective the date hereof and shall immediately terminate upon the earlier of (x) the termination of the Business Combination Agreement pursuant to its terms and (y) the date on which none of the Company, SPAC or any holder of a Locked-Up Share has any rights or obligations hereunder; provided that, in the event that the Business Combination Agreement is not terminated pursuant to its terms prior to the Closing, Article II, Article III and Article IV shall terminate upon the Closing. The termination of this Agreement shall not relieve any party from any liability arising in respect of any willful and material breach of this Agreement prior to such termination. Upon the termination of this Agreement (or any portion thereof), this Article VI shall survive indefinitely.

[Signature pages follow]

IN WITNESS WHEREOF, each party has duly executed and delivered this Agreement as a deed, all as of the date first written above.