You can buy any firearm you want without an ID. Just have to go to the right places
Seriously though. In Louisiana you can sell a handgun or rifle to another person, face to face, without a background check or any sort of paperwork. You just have to have reasonable belief that the person is not a felon and know that they are a resident of LA and are of proper age. So really, you *need* to show your ID to execute a proper exchange.