I have a potentially funny/potentially angsty scenario to run by you out of curiosity.
So, Lucifer has never used his workshop at the hotel, right? What if one day out of the blue, he has the sudden impulse to finally go into his workshop for the first time in months?
It's just another one of those days where he has nothing to really do around the hotel, so he randomly decides to go to see how much time he can kill in the workshop. He doesn't intend to be in there long, and everyone else is busy, so he doesn't bother telling anybody where he's going. Why should he? It's only going to be for a few minutes, a half hour at most. Why, he doesn’t even bother bringing his phone with him, and besides, the battery's dead and needs to charge anyway. Damn adhd/depression combo.
So Lucifer, without telling anybody where he's going, pays a visit to the workshop that hasn't gotten any use since it was made. The workshop that the majority of the hotel residents and staff have probably either forgotten was there or never knew existed in the first place. He's only expecting to be in there a short while, maybe do a little painting, maybe a little crafting, maybe a little tinkering. Just futz about for a bit until lunchtime rolls around...
He ends up unexpectedly hyperfixating like crazy and doesn't leave the workshop for a minimum of three days.
How long does it take for anybody to find him?
Who is it that does eventually find him?
In the event that nobody finds him because nobody thinks to check the hotel workshop, how long does it take for Lucifer to come out of his fugue state and re-emerge on his own?
And finally, when Lucifer does stumble his way back to rejoin society - probably very tired, very hungry, and very much in need of a shower - how much trouble is he in with the rest of the hotel? Particularly Charlie and Alastor?
What is the project Lucifer ends up hyperfixating on?
Apologies for the late answer, I've been out of town.
I can't go into the workshop too much because it will end up as a plot point. But!
How long does it take for anybody to find him?
That evening. Lucifer might have to spend a night or two wondering where Alastor is, Alastor has no such patience and will find him. There is no hiding in the hotel from Alastor.
Who is it that does eventually find him?
Alastor because he’s just getting used to sleeping with someone else and he’s not about to stop now.
In the event that nobody finds him because nobody thinks to check the hotel workshop, how long does it take for Lucifer to come out of his fugue state and re-emerge on his own?
Alastor would absolutely find him, but his record for hyperfocus is well over a year, and in that case, he only snapped out of it because he was running out of room for ducks.
And finally, when Lucifer does stumble his way back to rejoin society - probably very tired, very hungry, and very much in need of a shower - how much trouble is he in with the rest of the hotel? Particularly Charlie and Alastor?
Charlie would be filled with anxious concern and care. Alastor would physically pick him up and carry him to the shower, complaining the entire time about how he stinks, how dare he do this to them all, does he have any idea how concerned Charlie was for him, such disrespect, look at the state of your hair, have you no shame...
What is the project Lucifer ends up hyperfixating on?
How to fix a sentient broken microphone.