Restore Our Parks and Public Lands Act This bill establishes the National Park Service and Public Lands Legacy Restoration Fund into which, through FY2024, there shall be deposited an amount equal to 50% of all energy development revenues due and payable to the federal government from oil, gas, coal, or alternative or renewable energy development on federal lands and waters that would otherwise be credited, covered, or deposited as miscellaneous receipts under federal law. Deposited amounts must not exceed $1.3 billion for any such fiscal year. From such amounts 80% shall be allocated to the National Park Service for priority deferred maintenance projects, ensuring parity between transportation and nontransportation projects; 10% shall be allocated for the national wildlife refuge system maintenance backlog; 5% shall be allocated for addressing the public access and recreation backlog on public lands; and 5% shall be allocated for addressing the Bureau of Indian Education school construction and deferred maintenance backlogs. The Department of the Interior must take into consideration the projected lifespan of any projects under this bill when prioritizing which of those projects to fund. No more than 10% of amounts in the fund may be used for administrative costs. None of the amounts in the fund may be used for the acquisition of land or for supplanting discretionary funding for annually recurring facility operations, maintenance, and construction needs. Interior must submit to Congress, with the President's annual budget submission, a list of projects receiving allocations from the fund and a description of each such project. Interior, and other specified agencies, may accept cash or in-kind donations that advance efforts to reduce maintenance backlogs and encourage public-private partnerships.