Letter Agreement, dated as of October 13, 2021, among the Company, its officers and directors and the Sponsor

Exhibit 10.2

October 13, 2021

Black Mountain Acquisition Corp.

425 Houston Street, Suite 400

Fort Worth, TX 76102

EarlyBirdCapital, Inc.

366 Madison Ave 8th Floor

New York, NY 10017

Re: Initial Public Offering

Ladies and Gentlemen:

This letter (this “Letter Agreement”) is being delivered to you in accordance with the Underwriting Agreement (the “Underwriting Agreement”) entered into by and among Black Mountain Acquisition Corp., a Delaware corporation (the “Company”), and EarlyBirdCapital, Inc. and Stephens Inc. (the “Representatives”), as representatives of the underwriters (the “Underwriters”), relating to an underwritten initial public offering (the “Public Offering”), of 24,000,000 of the Company’s units (including up to an additional 3,600,000 units which may be purchased to cover over-allotments, if any) (the “Units”), each comprised of one share of the Company’s Class A common stock, par value $0.0001 per share (the “Class A Common Stock”), and three quarters of one warrant (each whole warrant, a “Warrant”). Each Warrant entitles the holder thereof to purchase one share of the Class A Common Stock at a price of $11.50 per share, subject to adjustment. The Units shall be sold in the Public Offering pursuant to the registration statement on Form S-1 (File No. 333-259469) and prospectus (the “Prospectus”) filed by the Company with the U.S. Securities and Exchange Commission (the “Commission”) and the Company shall apply to have the Units listed on the New York Stock Exchange. Certain capitalized terms used herein are defined in paragraph 11 hereof.

In order to induce the Company and the Underwriters to enter into the Underwriting Agreement and to proceed with the Public Offering and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, Black Mountain Sponsor LLC, a Delaware limited liability company (the “Sponsor”), and each of the undersigned individuals, each of whom is a member of the Company’s board of directors and/or management team (each an “Insider” and, collectively, the “Insiders”), hereby agrees with the Company as follows:

1. The Sponsor and each Insider agrees that if the Company seeks stockholder approval of a proposed Business Combination, then in connection with such proposed Business Combination, it or he shall vote any shares of Common Stock (as defined below) owned by it, him or her in favor of any proposed Business Combination. If the Company engages in a tender offer in connection with any proposed Business Combination, the Sponsor and each Insider agrees that it or he will not seek to sell its or his shares of Common Stock to the Company in connection with such tender offer.

2. The Sponsor and each Insider hereby agrees that in the event that the Company fails to consummate a Business Combination within the timeframe set forth in the Company’s amended and restated certificate of incorporation (as it may be amended from time to time, the “Charter”),

the Sponsor and each Insider shall take all reasonable steps to cause the Company to (a) cease all operations except for the purpose of winding up, (b) as promptly as reasonably possible but not more than ten (10) business days thereafter, subject to lawfully available funds therefor, redeem 100% of the Class A Common Stock sold as part of the Units in the Public Offering (the “Offering Shares”), at a per-share price, payable in cash, equal to the aggregate amount then on deposit in the Trust Account, including interest earned on the funds held in the Trust Account and not previously released to the Company to pay its taxes (less up to $100,000 of interest to pay dissolution expenses), divided by the number of then outstanding Offering Shares, which redemption will completely extinguish the Public Stockholders’ rights as stockholders (including the right to receive further liquidating distributions, if any), subject to applicable law, and (c) as promptly as reasonably possible following such redemption, subject to the approval of the Company’s remaining stockholders and the Company’s board of directors, dissolve and liquidate, subject in each case to the Company’s obligations under Delaware law to provide for claims of creditors and other requirements of applicable law. The Sponsor and the Insiders agree to not propose any amendment to the Company’s Charter that would affect the substance or timing of the Company’s obligation to redeem 100% of the Offering Shares if the Company does not complete a Business Combination within the required time period set forth in the Charter, unless the Company provides its Public Stockholders with the opportunity to redeem their Offering Shares upon approval of any such amendment at a per share price, payable in cash, equal to the aggregate amount then on deposit in the Trust Account including interest earned on the funds held in the Trust Account and not previously released to the Company to pay its taxes, divided by the number of then outstanding Offering Shares.

To the fullest extent permitted by applicable law, the Company hereby agrees to defend, indemnify, hold harmless and exonerate (including the advancement of expenses to the fullest extent permitted by applicable law) the Sponsor, its affiliates and their respective present and former officers and directors (each, a “Sponsor Indemnitee”) from any and all costs, fees, expenses, judgments, liabilities, fines, penalties, reasonable attorneys’ fees and amounts paid in settlement (including all interest, assessments and other charges paid or payable in connection with or in respect of such costs, fees, expenses, judgments, liabilities, fines, penalties and amounts paid in settlement) actually, and reasonably, incurred by a Sponsor Indemnitee or on a Sponsor Indemnitee’s behalf in connection with any threatened, pending or completed action, suit, arbitration, mediation, alternate dispute resolution mechanism, investigation, inquiry, hearing or any other actual, threatened or completed proceeding instituted by the Company or any third party, whether civil, criminal, administrative or investigative in nature, in respect of any investment opportunities sourced by a Sponsor Indemnitee for the Company or any liability arising with respect to a Sponsor Indemnitee’s activities in connection with the affairs of the Company (in each case to the extent that such indemnification, hold harmless and exoneration obligations with respect to such matters are not expressly covered by a separate written agreement between the Company and the applicable Sponsor Indemnitee); provided, that in no event shall a Sponsor Indemnitee be entitled to be indemnified or held harmless hereunder in respect of any costs, fees, expenses, judgments, liabilities, fines, penalties and amounts paid in settlement (if any) that Sponsor Indemnitee may incur by reason of such person’s own actual fraud or intentional misconduct; provided further, for the avoidance of doubt, that under no circumstance shall a Sponsor Indemnitee have a claim to any monies or assets held in the Trust Account, and the Company shall not be permitted to procure monies or assets held in the Trust Account for the satisfaction of its obligations to any Sponsor Indemnitee in respect of the indemnification provided hereunder. The Sponsor Indemnitees shall be third party beneficiaries of this paragraph.

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3. During the period commencing on the effective date of the Underwriting Agreement and ending 180 days after such date, the undersigned shall not, without the prior written consent of the Representatives, (a) 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 Securities Exchange Act of 1934, as amended (the “Exchange Act”), and the rules and regulations of the Commission promulgated thereunder, any Units, shares of Class A Common Stock, shares of the Company’s Class B common stock, par value $0.0001 per share (the “Class B Common Stock” and, together with the Class A Common Stock, the “Common Stock”), Warrants or any securities convertible into, or exercisable, or exchangeable for, shares of Common Stock owned by it, him or her, (b) 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 Units, shares of Common Stock, Warrants or any securities convertible into, or exercisable, or exchangeable for, shares of Class A Common Stock owned by it, him or her, whether any such transaction is to be settled by delivery of such securities, in cash or otherwise, or (c) publicly announce any intention to effect any transaction specified in clause (a) or (b).

4. In the event of the liquidation of the Trust Account, the Sponsor (which for purposes of clarification shall not extend to any officer, member or manager of the Sponsor) agrees to indemnify and hold harmless the Company against any and all loss, liability, claim, damage and expense whatsoever (including, but not limited to, any and all legal or other expenses reasonably incurred in investigating, preparing or defending against any litigation, whether pending or threatened, or any claim whatsoever) to which the Company may become subject as a result of any claim by (a) any third party (other than the Company’s independent registered public accounting firm) for services rendered or products sold to the Company or (b) a prospective target business with which the Company has entered into a letter of intent, confidentiality or other similar agreement or business combination agreement (a “Target”); provided, however, that such indemnification of the Company by the Sponsor shall apply only to the extent necessary to ensure that such claims by a third party for services rendered (other than the Company’s independent registered public accounting firm) or products sold to the Company or a Target do not reduce the amount of funds in the Trust Account to below the lesser of (A) $10.20 per share of the Offering Shares and (B) the actual amount per share of the Offering Shares held in the Trust Account due to reductions in the value of the trust assets as of the date of the liquidation of the Trust Account, in each case including interest earned on the funds held in the Trust Account and not previously released to the Company to pay its taxes, less taxes payable, except as to any claims by a third party or Target that executed an agreement waiving claims against and all rights to seek access to the Trust Account whether or not such agreement is enforceable. In the event that any such executed waiver is deemed to be unenforceable against such third party, the Sponsor shall not be responsible for any liability as a result of any such third party claims. Notwithstanding any of the foregoing, such indemnification of the Company by the Sponsor shall not apply as to any claims under the Company’s obligation to indemnify the Underwriters against certain liabilities, including liabilities under the Securities Act of 1933, as amended. The Sponsor shall have the right to defend against any such claim with counsel of its choice reasonably satisfactory to the Company if, within fifteen (15) days following written receipt of notice of the claim to the Sponsor, the Sponsor notifies the Company in writing that it shall undertake such defense.

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5. The Sponsor and each Insider acknowledges that it, he or she has no right, title, interest or claim of any kind in or to any monies held in the Trust Account or any other asset of the Company as a result of any liquidation of the Company with respect to the Founder Shares. The Sponsor and each Insider hereby further waives, with respect to any shares of the Common Stock held by it, him or her, (i) any claim they may have in the future as a result of, or arising out of, any contracts or agreements with the Company and will not seek recourse against the Trust Account for any reason whatsoever and (ii) redemption rights it, he or she may have in connection with the consummation of a Business Combination, including, without limitation, any such rights available in the context of a stockholder vote to approve such Business Combination or in the context of a tender offer made by the Company to purchase shares of the Common Stock and in connection with a stockholder vote to amend the Company’s Amended and Restated Certificate of Incorporation in a manner that would affect the substance or timing of the Company’s obligation to redeem 100% of the Common Stock if the Company has not consummated a Business Combination within 18 months from the closing of the Public Offering; provided, however, in each case, that the Sponsor, the Insiders and their respective affiliates shall be entitled to redemption and liquidation rights with respect to any shares of the Common Stock (other than the Founder Shares) it or they hold, including any claims or other recourse against the Trust Account they may have in respect of such rights, if the Company fails to consummate a Business Combination within 18 months from the date of the closing of the Public Offering or such later date as may be specified in an amendment to the Company’s Amended and Restated Certificate of Incorporation).

6. To the extent that the Underwriters do not exercise their over-allotment option to purchase an additional 3,600,000 Units (as described in the Prospectus), the Sponsor agrees, upon the expiration or waiver of such option, to forfeit, for cancellation at no cost, a number of Founder Shares equal to 900,000 multiplied by a fraction, (a) the numerator of which is 3,600,000 minus the number of Units purchased by the Underwriters upon the exercise of their over-allotment option, and (b) the denominator of which is 3,600,000. The forfeiture will be adjusted to the extent that the over-allotment option is not exercised in full by the Underwriters so that the Founder Shares will represent 20.0% of the Company’s issued and outstanding shares of Common Stock after the Public Offering. The Sponsor further agrees that to the extent that (a) the size of the Public Offering is increased or decreased and (b) the Sponsor has either purchased or sold shares of Common Stock or an adjustment to the number of Founder Shares has been effected by way of a stock split, stock dividend, reverse stock split, contribution back to capital or otherwise, in each case in connection with such increase or decrease in the size of the Public Offering, then (i) the references to 3,600,000 in the numerator and denominator of the formula in the first sentence of this paragraph shall be changed to a number equal to 15.0% of the number of the Units issued in the Public Offering and (ii) the reference to 900,000 in the formula set forth in the first sentence of this paragraph shall be adjusted to such number of Founder Shares that the Sponsor would have to collectively return to the Company in order for all holders of Founder Shares to hold an aggregate of 20.0% of the Company’s issued and outstanding shares of Common Stock after the Public Offering.

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6. Each of the Sponsor and each Insider hereby agrees and acknowledges that: (a) each of the Underwriters and the Company would be irreparably injured in the event of a breach by such Sponsor or Insider of his or its obligations under paragraphs 7(a) and 7(b), (b) monetary damages may not be an adequate remedy for such breach and (c) the non-breaching party shall be entitled to injunctive relief, in addition to any other remedy that such party may have in law or in equity, in the event of such breach.

7. (a) Subject to the exceptions set forth herein, the Sponsor and each Insider agrees that it or he shall not Transfer any Founder Shares held by it, him or her until the earlier to occur of (a) 180 days after completion of a Business Combination or (b) subsequent to a Business Combination, the date on which the Company consummates a subsequent liquidation, merger, stock exchange or other similar transaction which results in all of the Company’s stockholders having the right to exchange their shares of Common Stock for cash, securities or other property (the “Lock-up”).

(b) Subject to the exceptions set forth herein, the Sponsor and each Insider agrees that it or he shall not Transfer any Private Placement Warrants or Class A Common Stock underlying such Warrants held by it, him or her, until thirty (30) days after the completion of a Business Combination.

(c) Notwithstanding the provisions set forth in paragraphs 7(a) and 7(b) above, Transfers of the Founder Shares, Private Placement Warrants and shares of Class A Common Stock underlying the Private Placement Warrants are permitted (a) to the Company’s officers or directors, any affiliates or family members of any of the Company’s officers or directors, any members of the Sponsor or their affiliates, or any affiliates of the Sponsor; (b) in the case of an individual, by gift to a member of the individual’s immediate family, to a trust, the beneficiary of which is a member of the individual’s immediate family or an affiliate of such person, or to a charitable organization; (c) in the case of an individual, by virtue of laws of descent and distribution upon death of the individual; (d) in the case of an individual, pursuant to a qualified domestic relations order; (e) by private sales or transfers made in connection with the consummation of a Business Combination at prices no greater than the price at which the securities were originally purchased; (f) in the event of the Company’s liquidation prior to the completion of a Business Combination; (g) by virtue of the laws of Delaware or our Sponsor’s limited liability company agreement upon dissolution of our Sponsor; or (h) in the event of completion of a liquidation, merger, stock exchange or other similar transaction which results in all of the Company’s stockholders having the right to exchange their shares of Common Stock for cash, securities or other property subsequent to the completion of a Business Combination; provided, however, that in the case of clauses (a) through (e) and (g), these permitted transferees must enter into a written agreement agreeing to be bound by these transfer restrictions and the other restrictions contained in this Letter Agreement (including provisions relating to voting, the Trust Account and liquidating distributions).

8. Each Insider’s biographical information furnished to the Company that is included in the Prospectus is true and accurate in all respects and does not omit any material information with respect to such Insider’s background. Each Insider’s questionnaire furnished to the Company is true and accurate in all respects. Each Insider represents and warrants that: such Insider is not subject to or a respondent in any legal action for, any injunction, cease-and-desist order or order or stipulation to desist or refrain from any act or practice relating to the offering of securities in any jurisdiction; such Insider has never been convicted of, or pleaded guilty to, any crime (a)

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involving fraud, (b) relating to any financial transaction or handling of funds of another person, or (c) pertaining to any dealings in any securities and such Insider is not currently a defendant in any such criminal proceeding; and neither such Insider nor the Sponsor has ever been suspended or expelled from membership in any securities or commodities exchange or association or had a securities or commodities license or registration denied, suspended or revoked.

9. Except as disclosed in the Prospectus, neither the Sponsor nor any Insider nor any affiliate of the Sponsor or any Insider, nor any director or officer of the Company, shall receive from the Company any finder’s fee, reimbursement, consulting fee, monies in respect of any repayment of a loan or other compensation prior to, or in connection with any services rendered in order to effectuate the consummation of the Company’s initial Business Combination (regardless of the type of transaction that it is), other than the following, none of which will be made from the proceeds held in the Trust Account prior to the completion of the initial Business Combination: repayment of a loan and advances up to an aggregate of $250,000 made to the Company by the Sponsor; payment to the Sponsor or an affiliate of the Sponsor for office space, utilities and secretarial and administrative support for a total of $10,000 per month; reimbursement for any out-of-pocket expenses related to identifying, investigating, negotiating and completing an initial Business Combination; and repayment of non-interest bearing loans, if any, and on such terms as to be determined by the Company from time to time, made by the Sponsor or any of the Company’s officers or directors to finance transaction costs in connection with an intended initial Business Combination, provided, that, if the Company does not consummate an initial Business Combination, a portion of the working capital held outside the Trust Account may be used by the Company to repay such loaned amounts so long as no proceeds from the Trust Account are used for such repayment. Up to $1,500,000 of such loans may be convertible into warrants at a price of $1.00 per warrant at the option of the lender. Such warrants would be identical to the Private Placement Warrants, including as to exercise price, exercisability and exercise period.

10. The Sponsor and each Insider has full right and power, without violating any agreement to which it is bound (including, without limitation, any non-competition or non-solicitation agreement with any employer or former employer), to enter into this Letter Agreement and, as applicable, to serve as an officer and/or director on the board of directors of the Company and each Insider hereby consents to being named in the Prospectus as an officer and/or director of the Company, as applicable.

11. As used herein, (a) “Business Combination” shall mean a merger, capital stock exchange, asset acquisition, stock purchase, reorganization or similar business combination, involving the Company and one or more businesses; (b) “Founder Shares” shall mean the shares of the Class B Common Stock (and any shares of Class A Common Stock such shares are converted into) held by the Sponsor, the Company’s independent directors and any other holder prior to the consummation of the Public Offering; (c) “Private Placement Warrants” shall mean the warrants to purchase 11,600,000 shares of Class A Common Stock (or 13,040,000 shares of Class A Common Stock if the Underwriters’ over-allotment option in connection with the Public Offering is exercised in full), that the Sponsor has agreed to purchase for an aggregate purchase price of approximately $11,600,000(or approximately $13,040,000 if the Underwriters’ over-allotment option in connection with the Public Offering is exercised in full), or $1.00 per warrant, in a private placement that shall occur simultaneously with the consummation of the Public Offering; (d) “Public Stockholders” shall mean the holders of shares of Class A Common Stock

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issued in the Public Offering; (e) “Trust Account” shall mean the trust fund into which a portion of the net proceeds of the Public Offering and the sale of the Private Placement Warrants to the Sponsor shall be deposited; and (f) “Transfer” shall mean the (A) sale of, offer to sell, contract or agreement to sell, hypothecate, pledge, grant of any option to purchase or otherwise dispose of or agreement to dispose of, directly or indirectly, or establishment or increase of a put equivalent position or liquidation with respect to or decrease of a call equivalent position within the meaning of Section 16 of the Exchange Act, and the rules and regulations of the Commission promulgated thereunder with respect to, any security, (B) entry into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of any security, whether any such transaction is to be settled by delivery of such securities, in cash or otherwise, or (C) public announcement of any intention to effect any transaction specified in clause (A) or (B).

12. This Letter Agreement constitutes the entire agreement and understanding of the parties hereto in respect of the subject matter hereof and supersedes all prior understandings, agreements, or representations by or among the parties hereto, written or oral, to the extent they relate in any way to the subject matter hereof or the transactions contemplated hereby. This Letter Agreement may not be changed, amended, modified or waived (other than to correct a typographical error) as to any particular provision, except by a written instrument executed by all parties hereto.

13. No party hereto may assign either this Letter Agreement or any of its rights, interests, or obligations hereunder without the prior written consent of the other parties. Any purported assignment in violation of this paragraph shall be void and ineffectual and shall not operate to transfer or assign any interest or title to the purported assignee. This Letter Agreement shall be binding on the Sponsor, each Insider and each of their respective successors, heirs and assigns.

14. Nothing in this Letter Agreement shall be construed to confer upon, or give to, any person or entity other than the parties hereto any right, remedy or claim under or by reason of this Letter Agreement or of any covenant, condition, stipulation, promise or agreement hereof. All covenants, conditions, stipulations, promises and agreements contained in this Letter Agreement shall be for the sole and exclusive benefit of the parties hereto and their successors, heirs, personal representatives and assigns and permitted transferees.

15. This Letter Agreement may be executed in any number of original or facsimile counterparts and each of such counterparts shall for all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument.

16. This Letter Agreement shall be deemed severable, and the invalidity or unenforceability of any term or provision hereof shall not affect the validity or enforceability of this Letter Agreement or of any other term or provision hereof. Furthermore, in lieu of any such invalid or unenforceable term or provision, the parties hereto intend that there shall be added as a part of this Letter Agreement a provision as similar in terms to such invalid or unenforceable provision as may be possible and be valid and enforceable.

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17. This Letter Agreement shall be governed by and construed and enforced in accordance with the laws of the State of New York, without giving effect to conflicts of law principles that would result in the application of the substantive laws of another jurisdiction. The parties hereto (a) all agree that any action, proceeding, claim or dispute arising out of, or relating in any way to, this Letter Agreement shall be brought and enforced in the courts of New York City, in the State of New York, and irrevocably submit to such jurisdiction and venue, which jurisdiction and venue shall be exclusive and (b) waive any objection to such exclusive jurisdiction and venue or that such courts represent an inconvenient forum.

18. Any notice, consent or request to be given in connection with any of the terms or provisions of this Letter Agreement shall be in writing and shall be sent by express mail or similar private courier service, by certified mail (return receipt requested), by hand delivery or facsimile transmission.

19. This Letter Agreement shall terminate on the earlier of (a) the expiration of the Lock-up or (b) the liquidation of the Company; provided, however, that this Letter Agreement shall earlier terminate in the event that the Public Offering is not consummated and closed by January 5, 2022, provided further that paragraph 4 of this Letter Agreement shall survive such liquidation.

20. Each of the undersigned acknowledges and understands that the Underwriters and the Company will rely upon the agreements, representations and warranties set forth herein in proceeding with the Public Offering. Further, each of the undersigned hereby acknowledges and agrees that the Representatives on behalf of the Underwriters are third party beneficiaries of this Letter Agreement. Nothing contained herein shall be deemed to render the Underwriters a representative of, or a fiduciary with respect to, the Company, its stockholders or any creditor or vendor of the Company with respect to the subject matter hereof.

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[Signature Page to Letter Agreement]

Acknowledged and Agreed:

BLACK MOUNTAIN ACQUISITION CORP.

[Signature Page to Letter Agreement]