Some may debateif "other lawful purpose" would cover someone carrying in accordance with all other laws. Anyone who tries it may wind up being a test case. If your federal gov't property happens to be a post office by chance though, per 39 CFR 232.1 it is prohibited except for official purposes.
39 CFR 232.1
Weapons and explosives. Notwithstanding the provisions of any other law, rule or regulation, no person while on postal property may carry firearms, other dangerous or deadly weapons, or explosives, either openly or concealed, or store the same on postal property, except for official purposes.