Letter agreement with Aston Capital and Robert V. LaPenta

Exhibit 10.4

November 4, 2019

LGL Systems Acquisition Corp.

165 W. Liberty St., Suite 220

Reno, NV 89501

Jefferies LLC

520 Madison Avenue, 2^nd Floor

New York, New York 10022

Ladies and Gentlemen:

Each of the undersigned hereby agrees that until the earliest of an initial merger, share exchange, asset acquisition, stock purchase, recapitalization, reorganization or other similar business combination (a “business combination”) by LGL Systems Acquisition Corp. (the “Company”) or the Company’s liquidation, the undersigned shall seek to source and shall present to the Company for its consideration, prior to presentation to any other entity, any potential investment or acquisition opportunity in a business or businesses having an enterprise value at least equal to $350 million, subject to any pre-existing fiduciary or contractual obligations the undersigned may have, and will not enter into any agreement to purchase or invest in such business or businesses, unless the Company determines not to pursue such potential acquisition.

Robert V. LaPenta hereby agrees not to become an officer or director of any other special purpose acquisition company with a class of securities intended to be registered under the Securities Exchange Act of 1934, as amended, which has publicly filed a registration statement with the U.S. Securities and Exchange Commission until the Company has entered into a definitive agreement regarding an initial business combination or the Company has failed to complete an initial business combination within the time period required by its amended and restated certificate of incorporation, as it may be amended from time to time.

Each of the undersigned hereby acknowledges that the Company has established a trust account (the “Trust Account”) containing the proceeds of its initial public offering (the “IPO”) and from certain private placements occurring simultaneously with the IPO (including interest accrued from time to time thereon) for the benefit of the Company’s public stockholders and certain other parties (including the underwriters of the IPO). For and in consideration of the Company entering into this Agreement, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, each of the undersigned hereby agrees that it or he does not now and shall not at any time hereafter have any right, title, interest or claim of any kind in or to any assets held in the Trust Account, and shall not make any claim against the Trust Account, regardless of whether such claim arises as a result of, in connection with or relating in any way to this Agreement or any other matter, and regardless of whether such claim arises based on contract, tort, equity or any other theory of legal liability (any and all such claims are collectively referred to hereafter as the “Released Claims”). Each of the undersigned hereby irrevocably waives any Released Claims that it may have against the Trust Account now or in the future as a result of, or arising out of, any negotiations, contracts or agreements with the Company and will not seek recourse against the Trust Account for any reason whatsoever.

This Agreement shall become effective on the date first written above and shall remain in effect for a period to expire on the earlier of (i) the consummation by the Company of its initial business combination or (ii) the Company’s liquidation.

This 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. This 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.