EBC FOUNDER SHARES PURCHASE LETTER AGREEMENT BETWEEN REGISTRANT AND EARLYBIRDCAPITAL, INC

Exhibit 10.2

EARLYBIRDCAPITAL, INC.

SUBSCRIPTION AGREEMENT

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June 23, 2026

Lucens Capital Acquisition Corp. I

c/o Suite 210, 2nd Floor, Windward III

Regatta Office Park, Grand Cayman

PO Box 500, KY1-1106

Dear Sirs:

The undersigned and/or its designees hereby offer to purchase and subscribe for an aggregate of 125,000 ordinary shares (“Shares”), par value $0.0001 per share, of Lucens Capital Acquisition Corp. I (the “Company”) for an aggregate purchase price, and total consideration, of $815.21 (or $0.00652174 per share). The Company agrees to issue the Shares in the name and the amount of each of the designees of the undersigned, pursuant to Schedule A attached hereto.

The undersigned and/or its designees represent and warrant that they have been advised that the Shares have not been registered under the Securities Act; that they are acquiring the Shares for their account for investment purposes only; that they have no present intention of selling or otherwise disposing of the Shares in violation of the securities laws of the United States; that they are “accredited investors” as defined by Rule 501 of Regulation D promulgated under the Securities Act of 1933, as amended; that pursuant to FINRA Rule 5110, the Shares will be subject to a 180-day lock-up period commencing on the effective date of the registration statement relating to the Company’s initial public offering (the “Lock-up Period”), and shall not be sold, transferred, assigned, pledged, or hypothecated, or be the subject of any hedging, short sale, derivative, put, or call transaction that would result in the effective economic disposition of such Shares in compliance with FINRA Rule 5110(e)(1) until the consummation of an initial business combination; and that they are familiar with the proposed business, management, financial condition and affairs of the Company. Notwithstanding the foregoing, the undersigned and the Company acknowledge and agree that, from and after the 180th day following the consummation by the Company of its initial business combination, the Shares shall not bear any restrictive legends relating thereto, and the Company shall cause its transfer agent to remove any such legends no later than 180 days after the consummation of the initial business combination.

This Letter shall be construed in accordance with and governed by the laws of the State of New York applicable to contracts wholly performed within the borders of such state, without giving effect to the conflict of law principles thereof.

SCHEDULE A

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Designees