Lawful Interstate Transportation of Firearms Act This bill amends the federal criminal code to revise provisions related to the interstate transportation of firearms and ammunition. An individual may transport a firearm between two places (e.g., states) where it is legal to possess, carry, or transport the firearm. During transport, the firearm must be unloaded and secured or securely stored. Additionally, an individual may transport ammunition, or a detachable magazine or feeding device, between two places where it is legal to possess, carry, or transport the ammunition, magazine, or feeding device. During transport, the ammunition, magazine, or feeding device must not be loaded into a firearm and must be securely stored. This bill prohibits the arrest or detention of an individual for a state or local firearm or ammunition violation unless there is probable cause to believe the individual failed to comply with the provisions of this bill.