Great American Outdoors Act This bill establishes the National Parks and Public Land Legacy Restoration Fund to support deferred maintenance projects on federal lands. For FY2021-FY2025, there shall be deposited into the fund an amount equal to 50% of all federal revenues from the development of oil, gas, coal, or alternative or renewable energy on federal lands and waters. Deposited amounts must not exceed $1.9 billion for any fiscal year. The fund must be used for priority deferred maintenance projects in specified systems that are administered by the National Park Service, the Forest Service, the U.S. Fish and Wildlife Service, the Bureau of Land Management, and the Bureau of Indian Education. The Government Accountability Office must report on the effect of the fund in reducing the backlog of priority deferred maintenance projects for the specified agencies. Additionally, the bill makes funding for the Land and Water Conservation Fund (LWCF) permanent. The President shall annually report to Congress specified details regarding the allocation of funds to the LWCF. Congress may provide for alternate allocations using specified procedures.