Exhibit 10.13

Amesite Operating Company
Lock-Up Letter Agreement

June [__], 2020

Laidlaw & Company (UK) Ltd.,

As representative of the several Underwriters

named in Schedule I hereto,

c/o Laidlaw & Company (UK) Ltd.
521 Fifth Avenue, 5^th Floor
New York, New York 10175

Re:        Proposed Public Offering by Amesite Operating Company.

Ladies and Gentlemen:

The undersigned, a securityholder of Amesite Operating Company, a Delaware corporation (the “Company”), understands that Laidlaw & Company (UK) Ltd. (the “Representative”), proposes to enter into an Underwriting Agreement (the “Underwriting Agreement”) with the Company providing for the public offering (the “Public Offering”) of shares of the Company’s common stock, par value $0.0001 per share (the “Common Stock”). In recognition of the benefit that such an offering will confer upon the undersigned as a securityholder of the Company, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the undersigned (or any affiliate of the undersigned or any person in privity with the undersigned or any affiliate of the undersigned) agrees with the Representative that, during a period commencing on the date hereof and ending on the 90th day after the date of the Underwriting Agreement (the “Lock-Up Period”), the undersigned will not, without the prior written consent of the Representative, directly or indirectly, (i) offer, pledge, sell or contract to sell, sell any option or contract to purchase, purchase any option or contract to sell, grant any option, right or warrant for the sale of, or otherwise dispose of or transfer any Common Stock or any securities convertible into or exchangeable or exercisable for Common Stock, whether now owned or hereafter acquired by the undersigned or with respect to which the undersigned has or hereafter acquires the power of disposition, or file, make any demand with respect to, cause to be filed, or exercise any right with respect to any registration statement under the Securities Act of 1933, as amended (the “Securities Act”), with respect to any of the foregoing (collectively, the “Lock-Up Securities”), (ii) enter into any swap or any other agreement or any transaction that transfers, in whole or in part, directly or indirectly, the economic consequence of ownership of 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 (iii) engage in any short selling of the Common Stock.

Notwithstanding the foregoing, and subject to the conditions below, the undersigned may transfer the Lock-Up Securities without the prior written consent of the Representative, provided that (1) the Representative receives a signed lock-up agreement for the balance of the lockup 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) such transfers are not required to be reported with the Securities and Exchange Commission in accordance with the Securities Exchange Act of 1934, as amended the (“Exchange Act”) under Section 16 or otherwise, and (4) neither the undersigned nor any donee, trustee, distributee or transferee, as the case may be, otherwise voluntarily effects any public filing or report or other public notice 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) as a distribution to limited partners or stockholders of the undersigned; or

(iv) to any investment fund or other entity controlled or managed by the undersigned; or

(v) transfers by will, other testamentary document or intestate succession to the legal representative, heir, beneficiary or a member of the immediate family of the undersigned.

In addition, this letter agreement shall not restrict the delivery of Common Stock to the undersigned upon vesting and settlement of restricted share units or exercise of options outstanding on the date hereof in accordance with their terms; provided, for the avoidance of doubt, that this letter agreement shall restrict the Common Stock delivered upon any such vesting, settlement or exercise.

Furthermore, the undersigned may sell shares of Common Stock purchased by the undersigned on the open market following the Public Offering if and only if (i) such sales are not required to be reported in any public report or filing with the Securities Exchange Commission in accordance with the Exchange Act under Section 16 or otherwise and (ii) neither the undersigned nor any purchaser of the Common Stock otherwise voluntarily effects any public filing or report or other public notice regarding such sales.

Notwithstanding anything in the first paragraph hereof, if:

(1) during the last 17 days of the Lock-Up Period, the Company issues an earnings release or material news or a material event relating to the Company occurs; or

(2) prior to the expiration of the Lock-Up Period, the Company announces that it will release earnings results or becomes aware that material news or a material event will occur during the 16-day period beginning on the last day of the Lock-Up Period,

the Representative may extend, by written notice to the Company, the restrictions imposed by this lock-up agreement until the expiration of the 18-day period beginning on the issuance of the earnings release or the occurrence of the material news or material event, as applicable.

The undersigned hereby acknowledges and agrees that written notice of any extension of the Lock-Up Period pursuant to the previous paragraph will be delivered by the Representative to the Company (in accordance with the notice section of the Underwriting Agreement) and that any such notice properly delivered will be deemed to have been given to, and received by, the undersigned. The undersigned further agrees that, prior to engaging in any transaction or taking any other action that is subject to the terms of this lock-up agreement during the period from the date of this lock-up agreement to and including the 34th day following the expiration of the initial Lock-Up Period, it will give notice thereof to the Company and will not consummate such transaction or take any such action unless it has received written confirmation from the Company that the Lock-Up Period (as may have been extended pursuant to the previous paragraph) has expired.

In furtherance of the foregoing, 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 and the Company and its transfer agent are hereby authorized to decline to make any transfer of Lock-Up Securities if such transfer would constitute a violation or breach of this agreement. In addition, the undersigned further agrees that (i) it will not, during the Lock-Up Period, make any demand or request for or exercise any right with respect to the registration under the Securities Act of any Lock-Up Securities.

This letter agreement shall automatically terminate if (i) the Company notifies the Representative in writing that it does not intend to proceed with the Public Offering, (ii) if the Underwriting Agreement is not executed prior to [ ], 2020 or (iii) if the Underwriting Agreement (other than the provisions thereof which survive termination) shall terminate or be terminated prior to payment for and delivery of the Common Stock to be sold thereunder.

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

[Signature Page Follows]