Firearm Owners Responsibility and Safety Act This bill establishes a framework to regulate the storage of firearms at the federal, state, and tribal levels. The bill also removes limitations on the civil liability of gun manufacturers and the disclosure of gun trace data in civil actions. Among its provisions, the bill generally requires firearms to be kept, left, or stored in a secure gun storage or safety device; requires the Department of Justice to award grants to states and tribes to implement firearms safe storage requirements that are functionally identical to the requirements established by this bill; repeals the Protection of Lawful Commerce in Arms Act, which prohibits civil actions against a firearm or ammunition manufacturer, seller, importer, dealer, or trade association for damages resulting from the criminal or unlawful misuse of a firearm; and allows firearms trace data maintained by the Bureau of Alcohol, Tobacco, Firearms and Explosives to be discoverable, admissible as evidence, and used, relied on, or disclosed in a civil action or administrative proceeding.