Exhibit 99.4

June 26, 2025

Alpha Capital Anstalt

Altenbach 8

9490 Vaduz, Liechtenstein

Ladies and Gentlemen:

Reference is made to that certain Securities Purchase Agreement, dated as of March 26, 2025 (the “Purchase Agreement”), by and among NLS Pharmaceutics Ltd., a corporation incorporated under the laws of Switzerland and including any successor Company thereto (the “Company”) and each of the other parties thereto. Capitalized terms used but not defined in this side letter (this “Letter”) shall have the meanings ascribed to them in the Purchase Agreement.

Pursuant to Section 4.31 of the Purchase Agreement, the Company agreed to issue to Alpha Capital Anstalt (“Alpha”) 435,000 Preferred Shares (the “Make Whole Shares”), to compensate Alpha for the Common Shares that would have been issued (the “Missing Shares”) to Alpha under the Debt SPA and the Securities Purchase Agreement entered into on December 4, 2025 (the “December SPA”), relating to an alleged claim that the Company did not timely honor its price-protection and registration obligations under the Debt SPA and December SPA, respectively.

Alpha hereby agrees to be issued pre-funded warrants to purchase 485,000 common shares (the “Pre-Funded Warrants”), in the form annexed hereto as Exhibit A. Alpha further agrees that the issuance of the Pre-Funded Warrants fully satisfies the compensation to Alpha for the Make Whole Shares under the Debt SPA, relating to an alleged claim under the Debt SPA and December SPA.

Assuming a cashless exercise of the Pre-Funded Warrants, the Company acknowledges that the holding period for Rule 144 purposes of the Common Shares issued upon exercise of the Pre-Funded Warrants will tack back to March 26, 2025.

[Signature Pages Follow]

Signature Page to Letter Agreement

Exhibit A

Form of Pre-Funded Warrant

See attached.