Exhibit 10.5


 


___________, 2020


 


LifeSci Acquisition II Corp.


250 W. 55th Street, #3401


New York, NY 10019


 


Ladies and Gentlemen:


 


LifeSci Acquisition
II Corp. (the “Company”), a blank check company formed for the purpose of acquiring one or more businesses or entities
(a “Business Combination”), intends to register its securities under the Securities Act of 1933, as amended (“Securities
Act”), in connection with its initial public offering (“IPO”), pursuant to a registration statement on Form S-1
(“Registration Statement”).


 


The undersigned
hereby commits that it will purchase an aggregate of 3,033,333 warrants (or up to 3,283,333 warrants if the over-allotment
option is exercised in full) of the Company (“Private Warrants”), at a price of $0.90 per warrant in the form
attached hereto as Exhibit A for an aggregate purchase price of $2,730,000 (the “Private Warrant Purchase
Price”).


 


At least twenty-four
(24) hours prior to the effective date of the Registration Statement, the undersigned will cause the Private Warrant Purchase Price
to be delivered to Loeb & Loeb, LLP (“Loeb”), as escrow agent, by wire transfer as set forth in the instructions
attached as Exhibit B to hold in a non-interest bearing account until the Company consummates the IPO.


 


The consummation of
the purchase and issuance of the Private Warrants shall occur simultaneously with the consummation of the IPO. Simultaneously with
the consummation of the IPO, Continental shall deposit the Private Warrant Purchase Price, without interest or deduction, into
the trust fund (“Trust Fund”) established by the Company for the benefit of the Company’s public stockholders
as described in the Registration Statement.


 


Each of the Company
and the undersigned acknowledges and agrees that Loeb is serving hereunder solely as a convenience to the parties to facilitate
the purchase of the Private Warrants.


 


Additionally, the undersigned
agrees:


 


		·	not to propose, or vote in favor of, an amendment to the Company’s Amended and Restated Certificate
of Incorporation that would affect the substance or timing of the Company’s obligation to redeem 100% of the Company’s
shares of Common Stock sold in the IPO if the Company does not complete an initial Business Combination within 24 months from the
closing of the IPO, unless the Company provides the holders of shares of Common Stock sold in the IPO with the opportunity to redeem
their shares of Common Stock upon approval of any such amendment at a per-share price, payable in cash, equal to the aggregate
amount of the Trust Fund, including interest earned on Trust Fund and not previously released to the Company to pay the Company’s
franchise and income taxes, divided by the number of then outstanding shares of Common Stock sold in the IPO;



 


		·	the undersigned will not participate in any liquidation distribution with respect to the Private
Warrants (but will participate in liquidation distributions with respect to any shares of Common Stock purchased
by the undersigned in the IPO or in the open market) if the Company fails to consummate a Business Combination;






 






     


     


    

 


		·	that the Private Warrants and underlying securities will not be transferable until after the consummation
of a Business Combination except (i) to the Company’s pre-IPO stockholders, or to the Company’s officers, directors,
advisors and employees, (ii) transfers to the undersigned’s affiliates or its members upon its liquidation, (iii) to relatives
and trusts for estate planning purposes, (iv) by virtue of the laws of descent and distribution upon death, (v) pursuant to a qualified
domestic relations order, (vi) by private sales at prices no greater than the price at which the Private Warrants were originally
purchased or (vii) to the Company for cancellation in connection with the consummation of a Business Combination, in each case
(except for clause vii) where the transferee agrees to the terms of the transfer restrictions; and



 


		·	the Private Warrants will include any additional terms or restrictions as is customary in other
similarly structured blank check company offerings or as may be reasonably required by the underwriters in the IPO in order to
consummate the IPO, each of which will be set forth in the Registration Statement.



 


The undersigned acknowledges
and agrees that the purchaser of the Private Warrants will execute agreements in form and substance typical for transactions of
this nature necessary to effectuate the foregoing agreements and obligations prior to the consummation of the IPO as are reasonably
acceptable to the undersigned, including but not limited to an insider letter.


 


The undersigned hereby
represents and warrants that:


 


(a)           
it has been advised that the Private Warrants have not been registered under the Securities Act;


 


(b)           
it will be acquiring the Private Warrants for its account for investment purposes only;


 


(c)           
it has no present intention of selling or otherwise disposing of the Private Warrants in violation of the securities
laws of the United States;


 


(d)           
it is an “accredited investor” as defined by Rule 501 of Regulation D promulgated under the Securities
Act of 1933, as amended;


 


(e)           
it has had both the opportunity to ask questions and receive answers from the officers and directors of the Company
and all persons acting on its behalf concerning the terms and conditions of the offer made hereunder;


 


(f)            
it is familiar with the proposed business, management, financial condition and affairs of the Company;


 









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(g)           it has full power, authority and legal capacity to execute and deliver this letter and any documents contemplated
herein or needed to consummate the transactions contemplated in this letter; and


 


(h)            this letter constitutes its legal, valid and binding obligation, and is enforceable against it.


 


This letter agreement
constitutes the entire agreement between the undersigned and the Company with respect to the purchase of the Private Warrants,
and supersedes all prior and contemporaneous understandings, agreements, representations and warranties, both written and oral,
with respect to the same.


 


	 	Very truly yours,
	 	 
	 	LIFESCI HOLDINGS LLC
	 	 
	 	By:	 
	 	 	Name:
	 	 	Title:




 




	Accepted and Agreed:	 
	 	 
	LIFESCI ACQUISITION II CORP.	 
	 	 
	By:	 	 
	 	Name:	Andrew McDonald	 
	 	Title:	Chief Executive Officer	 









 






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Exhibit A


 


Form of Warrant


 






     


     


    

 


Exhibit B


 


Wire Instructions