Exhibit 10.45

Form of Lock-Up Agreement

__________, 2020

H.C. Wainwright & Co., LLC

430 Park Avenue, 3rd Floor

New York, NY 10022

Ladies and Gentlemen:

The undersigned understands that H.C. Wainwright & Co., LLC, acting as placement agent (the “Placement Agent”) in an offering with Aptorum Group Limited, a Cayman Islands corporation, (the “Company”), proposes to enter into a placement agency agreement (the “Agency Agreement”), providing for the public offering (the “Public Offering”) of ordinary shares, par value $1.00 per share, of the Company (the “Shares”) and ordinary share purchase warrants (the “Warrants”).

To induce the Placement Agent to continue its efforts in connection with the Public Offering, the undersigned hereby agrees that, without the prior written consent of the Placement Agent, the undersigned will not, during the period commencing on the date hereof and ending ninety (90) days after the date of the final prospectus supplement (the “Prospectus”) relating to the Public Offering (the “Lock-Up Period”), (1) offer, pledge, sell, contract to sell, sell any option or contract to purchase, purchase any option or contract to sell, grant any option, right or warrant to purchase, or otherwise transfer or dispose of, directly or indirectly, any ordinary shares of the Company or any securities convertible into or exercisable or exchangeable for ordinary shares of the Company, whether now beneficially owned (as such term is used in Rule 13d-3 of the Securities Exchange Act of 1934, as amended (the “Exchange Act”) 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”); (2) enter into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of Lock-Up Securities, whether any such transaction is to be settled by delivery of shares of Lock-Up Securities, in cash or otherwise; (3) make any demand for or exercise any right with respect to the registration of any Lock-Up Securities; or (4) publicly disclose the intention to make any offer, sale, pledge or disposition, or to enter into any transaction, swap, hedge or other arrangement relating to any Lock-Up Securities. Notwithstanding the foregoing, and subject to the conditions below, the undersigned may transfer Lock-Up Securities without the prior written consent of the Placement Agent in connection with (a) transfers of Lock-Up Securities as a bona fide gift, by will or intestacy or to a family member or trust for the direct or indirect benefit of the undersigned or a family member (for purposes of this lock-up agreement, “family member” means any relationship by blood, marriage or adoption, not more remote than first cousin); (b) transfers of Lock-Up Securities to a charity or educational institution; (c) if the undersigned or a family member, directly or indirectly, controls a corporation, partnership, limited liability company or other business entity, any transfers of Lock-Up Securities to any shareholder, partner or member of, or owner of similar equity interests in, the undersigned, as the case may be; or (d) the sales of Shares to cover the payment of the exercise prices or the payment of taxes associated with the exercise or vesting of equity awards under any equity compensation plan of the Company; provided that in the case of any transfer pursuant to the foregoing clauses (a), (b) or (c), (i) any such transfer shall not involve a disposition for value, (ii) each transferee shall sign and deliver to the Placement Agent a lock-up agreement substantially in the form of this lock-up agreement and (iii) no filing under Section 16(a) of the Exchange Act shall be required or shall be voluntarily made, except for a Form 5. The undersigned also agrees and consents to the Company’s entry of stop transfer instructions with the Company’s transfer agent against the transfer of the undersigned’s Lock-Up Securities except in compliance with this lock-up agreement.

No provision in this agreement shall be deemed to restrict or prohibit the exercise, exchange or conversion by the undersigned of any securities exercisable or exchangeable for or convertible into Shares, as applicable; provided that the undersigned does not transfer the Shares acquired on such exercise, exchange or conversion during the Lock-Up Period, unless otherwise permitted pursuant to the terms of this lock-up agreement.

The undersigned understands that the Company and the Placement Agent are relying upon this lock-up agreement in proceeding toward consummation of the Public Offering. The undersigned further understands that this lock-up agreement is irrevocable and shall be binding upon the undersigned’s heirs, legal representative, successors and assigns.

The undersigned understands that, if the Agency Agreement is not executed by _______, 2020, or if the Agency Agreement (other than the provisions thereof which survive termination) shall terminate or be terminated prior to payment for and delivery of the Shares and Warrants to be sold thereunder, then this lock-up agreement shall be void and of no further force or effect.

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

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Very truly yours,

(Name - Please Print)

(Signature)

(Name of Signatory, in the case of entities - Please Print)

(Title of Signatory, in the case of entities - Please Print)

Address:

[Signature Page to Lock-Up Agreement]