Exhibit
10.10


 


Lock-up
Agreement


 


Cantor
Fitzgerald & Co.


499
Park Avenue


New
York, New York 10022


Attn:
Equity Capital Markets


 


Canaccord
Genuity LLC


99
High Street, Suite 1200


Boston,
Massachusetts 02110


Attn:
Equity Capital Markets


 


Re:
Proposed Initial Public Offering by Lucid Diagnostics Inc.


 


Ladies
and Gentlemen:


 


The
undersigned, a securityholder and/or officer and/or a director of Lucid Diagnostics Inc., a Delaware corporation (the “Company”),
understands that the Company proposes to enter into an Underwriting Agreement (the “Underwriting Agreement”) with
Cantor Fitzgerald & Co. and Canaccord Genuity LLC, as representatives of the several underwriters named therein (the “Representatives”)
relating to the proposed initial public offering (the “Offering”) of shares of the Company’s common stock, par
value $0.001 per share (the “Common Stock”). The undersigned acknowledges that the underwriters are relying on the
representations and agreements of the undersigned contained in this lock-up agreement in conducting the Offering and, at a subsequent
date, in entering into the Underwriting Agreement and other underwriting arrangements with the Company with respect to the Offering.


 


In
recognition of the benefit that the Offering will confer upon the undersigned as a securityholder and/or officer and/or a director of
the Company, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the undersigned
agrees that, during the period beginning on the date hereof and ending on the date that is 180 days from the date of the Underwriting
Agreement (the “Lock-Up Period”), the undersigned will not (and will cause any immediate family member not to), without
the prior written consent of each Representative, which may withhold its consent in its sole discretion, directly or indirectly, (i) sell,
offer to sell, contract to sell or lend, effect any short sale or establish or increase a Put Equivalent Position (as defined in Rule
16a-1(h) under the Securities Exchange Act of 1934, as amended (the “Exchange Act”)) or liquidate or decrease any
Call Equivalent Position (as defined in Rule 16a-1(b) under the Exchange Act), pledge, hypothecate or grant any security interest in,
or in any other way transfer or dispose of, any Common Stock or any securities convertible into or exchangeable or exercisable for Common
Stock, in each case whether now owned or hereafter acquired by the undersigned or with respect to which the undersigned has or hereafter
acquires the power of disposition (collectively, the “Lock-Up Securities”), (ii) make any demand for, or exercise
any right with respect to the registration of any of the Lock-Up Securities, or the filing of any registration statement, prospectus
or prospectus supplement (or an amendment or supplement thereto) in connection therewith, under the Securities Act of 1933, as amended,
(iii) enter into any swap, hedge or any other agreement or any transaction that transfers, in whole or in part, the economic consequence
of ownership of the Lock-Up Securities, whether any such swap or transaction is to be settled by delivery of Common Stock or other securities,
in cash or otherwise, or (iv) publicly announce the intention to do any of the foregoing.


 




    	 



     


    

 


Notwithstanding
the foregoing, and subject to the conditions below, the undersigned may transfer the Lock-Up Securities pursuant to clauses (i) through
(vii) below without the prior written consent of each Representative, provided that (1) prior to any such transfer,
other than in the case of clause (vii), the Representatives receive a signed lock-up agreement, substantially in the form of this lock-up
agreement, for the balance of the Lock-Up Period from each donee, trustee, distributee or transferee, as the case may be, (2) any
such transfer shall not involve a disposition for value, (3) in the case of clauses (i) through (iii) below, such transfers
are not required to be reported with the Securities and Exchange Commission under the Exchange Act, and (4) the undersigned does
not otherwise voluntarily effect any public filing or report regarding such transfers:


 


	 	(i)	as
    a bona fide gift or gifts; or
	 	 	 
	 	(ii)	to
    any trust for the direct or indirect benefit of the undersigned or the immediate family of the undersigned (for purposes of this
    lock-up agreement, “immediate family” shall mean any relationship by blood, marriage or adoption, not more remote than
    first cousin); or
	 	 	 
	 	(iii)	pursuant
    to a qualified domestic order or in connection with a divorce settlement; or
	 	 	 
	 	(iv)	by
    will or intestate succession to the legal representative, heir, beneficiary or immediate family of the undersigned upon the death
    of the undersigned; or
	 	 	 
	 	(v)	to
    a charity or educational institution; or
	 	 	 
	 	(vi)	to
    an affiliate or to an investment fund or any other entity controlled or managed by the undersigned, or to a shareholder, partner,
    or member of a corporation, partnership, or limited liability company controlled by the undersigned; or
	 	 	 
	 	(vii)	pursuant
    to forfeitures of Common Stock or any securities convertible into or exercisable or exchangeable for Common Stock to satisfy tax
    withholding obligations of the undersigned in connection with the vesting of restricted stock or stock options granted to the undersigned
    pursuant to the Company’s incentive equity plans.


 


No
provision of this lock-up agreement shall be deemed to restrict or prohibit the exercise or exchange by the undersigned of any option
or warrant to acquire shares of Common Stock, or other security exchangeable or exercisable for or convertible into Common Stock, provided
that the undersigned does not transfer the Common Stock acquired upon such exercise, exchange, or conversion during the Lock-Up Period
unless such transfer is otherwise permitted hereunder.


 




    	 



     


    

 


The
undersigned further agrees that the foregoing provisions shall be equally applicable to any Common Stock the undersigned may purchase
or otherwise receive in the Offering.


 


The
undersigned also agrees and consents to the entry of stop transfer instructions with the Company’s transfer agent and registrar
against the transfer of the Lock-Up Securities except in compliance with the foregoing restrictions.


 


With
respect to the Offering only, the undersigned waives any registration rights relating to registration under the Securities Act of the
offer and sale of any shares of Common Stock and/or any options or warrants or other rights to acquire Common Stock or any securities
exchangeable or exercisable for or convertible into Common Stock, or to acquire other securities or rights ultimately exchangeable or
exercisable for or convertible into Common Stock, owned either of record or beneficially by the undersigned, including any rights to
receive notice of the Offering.


 


In
addition, if the undersigned is an officer or director of the Company, (i) the Representatives agree that, at least three business days
before the effective date of any release or waiver of the foregoing restrictions in connection with a transfer of Shares, the Representatives
will notify the Company of the impending release or waiver, and (ii) the Company (in accordance with the provisions of the Underwriting
Agreement) will announce the impending release or waiver by press release through a major news service at least two business days before
the effective date of the release or waiver. Any release or waiver granted by the Representatives hereunder to any such officer or director
shall only be effective two business days after the publication date of such press release. The provisions of this paragraph will not
apply if both (a) the release or waiver is effected solely to permit a transfer not for consideration and (b) the transferee has agreed
in writing to be bound by the same terms described in this letter agreement that are applicable to the transferor to the extent and for
the duration that such terms remain in effect at the time of the transfer.


 


The
undersigned confirms that the undersigned has not, directly or indirectly, taken any action designed to or that might reasonably be expected
to cause or result in the stabilization or manipulation of the price of any security of the Company to facilitate the sale of the Common
Stock. The undersigned will not take, directly or indirectly, any such action.


 


As
used herein, “immediate family” shall mean the spouse, domestic partner, lineal descendant, father, mother, brother, sister,
or any other person with whom the undersigned has a relationship by blood, marriage or adoption not more remote than first cousin.


 


The
undersigned represents and warrants that the undersigned has full power, capacity and authority to enter into this letter agreement.
This letter agreement is irrevocable and will be binding on the undersigned and the successors, heirs, personal representatives and assigns
of the undersigned.


 


This
lock-up agreement shall be governed by and construed in accordance with the laws of the State of New York.


 


Whether
or not the Offering actually occurs depends on a number of factors, including market conditions. Any Offering will only be made pursuant
to an Underwriting Agreement, the terms of which are subject to negotiation between the Company and the underwriters.


 


This
lock-up agreement shall automatically terminate, and the undersigned shall be released from its obligations hereunder, upon the earliest
to occur, if any, of (i) the Company advising the Representatives in writing, prior to the execution of the Underwriting Agreement,
that it has determined not to proceed with the Offering, (ii) the executed Underwriting Agreement being terminated prior to the
closing of the Offering (other than the provisions thereof that survive termination), and (iii) October 31, 2021, in the event that the
Underwriting Agreement has not been executed by such date.


 


[Signature
Page Follows]


 




    	 



     


    

 


	 	Very truly yours,
	 	 	 
	 	
	 	Name of Securityholder/Director/Officer (Print exact name)
	 	 	                                         
	 	By:	
	 	 	Signature
	 	 	 
	 	If not signing in an individual capacity:
	 	 	 
	 	 
	 	Name of Authorized Signatory (Print)
	 	 	 
	 	 
	 	Title of Authorized Signatory (Print)
	 	(indicate capacity of person signing if signing as custodian, trustee or on behalf of an entity)