Localizing Authority of Management Plans Act of 2019 or the LAMP Act of 2019 This bill revises requirements governing the management of endangered or threatened species, establishes exemptions from environmental review requirements, and permits the delegation of authority for species management to states under certain circumstances. Specifically, this bill revises requirements governing cooperative management agreements to manage areas established for the conservation of endangered or threatened species. Under current law, the agreements are between states and the Department of the Interior or the Department of Commerce. This bill allows the departments to enter into (1) agreements with local governments, Indian tribes, or nonfederal persons; and (2) agreements to manage areas established for the conservation of species that are candidates for listing. The bill exempts the actions of preparing, approving, and entering into an agreement from environmental review requirements. The departments may (1) delegate the authority to manage species to states that establish and maintain an adequate program for the conservation of endangered or threatened species that reside in the state, and (2) provide financial assistance to a state that has entered into an agreement with the department or to a state with delegated authority.