I've only encountered a couple that needed a new nut, but it does happen - and if I'm being honest, I've cut 20 times more nuts for strats and teles
Most of the time you can get away with some light filing and shaping of the slot, and some lubrication - Nut sauce, Graphite, 3 in 1, etc
Once you get the nut situated, an LP (or any other TOM bridge guitar) is rock solid
I just think it's fucking hilarious when Glenn Fricker and other YouTubers have a heavy flow day about something that's "standard maintenance" for literally every guitar that's ever been made in human history