I joined a running campaign (still at the low levels) set in a magic library and I had a character with a comically egregious case of that kind of back story. The campaign had a tight foundation with everyone else already knowing each other and being there for a reason.

It wasn’t easy to recon me in, so we didn’t and I worked this out with the DM. I just had all these things I’d reference. Grand, level-inapproriate adventures, offering impossible feats as part of insane plans, being a key figure in historical events that the others were quite sure had never happened, etc. But absolutely no other sign of insanity or chronic lying in my serious, good-aligned, heroic character.

The DM let everyone have fun scratching their heads over it for a few sessions before they stumbled on my character’s series and found out he was just a fictional hero spawned by the library to assist their quest. His level was from the creation magic and had nothing to do with his real-only-to-him backstory.

It worked out in that very very specific setting.