Filed Pursuant to Rule 424(b)(3)

Registration No. 333-280011

HAMILTON LANE PRIVATE INFRASTRUCTURE FUND

SUPPLEMENT DATED JANUARY 9, 2026 TO

THE PROSPECTUS DATED AUGUST 1, 2025

Effective as of the date of this supplement, the following amends, supplements, or modifies certain information contained in the Prospectus of Hamilton Lane Private Infrastructure Fund (the “Fund”) dated August 1, 2025 (the “Prospectus”).

Board Approves Conversion to Interval Fund

The Fund’s Board of Trustees has approved the Fund’s undertaking of certain actions necessary for the Fund to operate as an “interval fund” in reliance on Rule 23c-3 under the Investment Company Act of 1940, as amended (the “1940 Act”), including, but not limited to, (i) the adoption of a fundamental policy to make quarterly repurchase offers pursuant to Rule 23c-3(b)(2)(i) under the 1940 Act, and (ii) authorization to prepare and file a post-effective amendment to the Fund’s registration statement on Form N-2 (the “Amendment”) to include, among other things, disclosure related to the Fund’s operation as an interval fund. Once the Amendment becomes effective, the Fund will begin to operate as an interval fund (the “Interval Fund Conversion”). The Fund will continue to offer its shares on a continuous basis at their net asset value per share prior to and following the Interval Fund Conversion, which is currently expected to occur in April 2026.

This Supplement, and each Prospectus and the Statement of Additional Information (the “SAI”) for Class R, Class I and Class Y Shares dated August 1, 2025, of the Fund provide relevant information for all shareholders. Each Prospectus and SAI of the Fund have been filed with the U.S. Securities and Exchange Commission, and are incorporated by reference. These can be obtained without charge by calling the Fund at (888)-882-8212 or by visiting www.hamiltonlane.com.

Investors Should Retain This Supplement for Future Reference