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Currently, there is no law that prohibits a person who can lawfully possess a firearm from having said firearm while living with someone who cannot possess a firearm. This means that there is no separate law dictating what requirements the lawful possessor must meet while leaving with a person who cannot possess a firearm (i.e., lock and key, etc).
The real issue is "possession." As you can tell, a convicted felon cannot possess a firearm. This means both "actual possession" (i.e., physically holding a firearm) and "constructive possession." Constructive possession occurs when a person, while not in physical possession of the firearm, still has the dominion and ability to control the firearm.
The prohibition against felons in possession of firearms applies to both actual and constructive possession. So keeping a firearm under lock and key, with no way for the felon to be able to control the firearm, removes the possibility of the felon from being charged with constructive possession of a firearm. Lock and key is not a per se requirement for the lawful owner of the firearm to meet, but is a procedural safeguard deterring the felon from constructively possessing the firearm.
Essentially, while there is no law requiring the firearm to be under lock and key at all times, the lock and key acts as a safeguard so prosecutors cannot charge the felon from being in constructive possession of the firearm.