Is there a safe way for someone to keep a gun in their house when they experience suicidal ideation?

I haven't done this for guns but put the key for the lock in a big block of ice so you have to wait until it thaws to get it. Alternatively you can dissemble the gun so you have to lookup the manual to make it ready for use. This just delays use by 15-30 minutes at best though so ymmv.

Practically speaking, pepper spray is the most effective self-defense outside of a gun. Maybe get a pepper ball gun if you need the extra range and you could also threaten someone attacking you into thinking it's a real gun?