LPOE Modernization Trust Fund Act This bill establishes the Land Port of Entry Modernization Trust Fund and addresses other issues related to U.S. ports of entry. The bill transfers specified amounts, including a portion of certain collected customs fees, to the trust fund each year. It also requires the Department of Homeland Security (DHS) and the Department of State to collect certain surcharges related to immigration and land border inspections, with a portion of the surcharges to be deposited into the trust fund. DHS may not seek to increase fees to offset the amounts transferred into the trust fund. Subject to appropriations, the amounts in the trust fund may be used to (1) construct new ports of entry, (2) expand and improve existing ports of entry, (3) procure technology for inspecting and processing traffic passing through ports of entry, and (4) hiring U.S. Customs and Border Protection staff. DHS must also establish the Land Port of Entry Modernization Oversight Board to advise DHS on how to use the trust fund and to review the trust fund's expenditures.