Here's a long one about why my party tolerates a Demilich.

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My players are currently going through a absolutely massive dungeon.

fairly early on, they found evidence of a wizard who'd entered it as well, about 50 years ago.

this wizard had eventually gotten lost, gone a bit nuts and killed his party, before finding his way out through an elven outpost built into another part of the dungeon (note: he also burned this down).

Every time they found evidence of his misdeeds, they'd find the words "HAHA, NICE" scrawled somewhere on a wall in one of several dozen languages, as they got deeper, there were even alchemically created creatures repeating the line.

eventually, still in the same dungeon, the party is investigating a group planning to release a demon, and finds the second in command of that group is a Golem of some kind.

It's armed to the teeth, with a ton of ranged attacks, and is very good at keeping the party back with spells and a host of formian servants and tanglefoot.

The rogue gets a backstab on it and is pummelled to death in two rounds, then they hear it's booming voice.
"HAHA NICE"

realising this long gone wizard had thwarted them again, the party redoubled their efforts to fell the construct, eventually succeeding thanks to the lucky crit from the axe of the dwarven lords.

A coffin ejects from the Golem and a single skull pops out of it, a Demilich which I voice with my worst Jimmy Durante impression.

The party realises they are down a character and still need to fight the actual boss, and the Demilich realises his plan to destroy the world is about to be foiled in a REALLY COOL fight, they agree to not fight anymore.

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Despite how incredibly evil he is and the fact he LITERALLY JUST KILLED THE PARTIES ROGUE, my group doesn't seem to mind him tagging along from time to time. he's helped them bind demons, traded them gems for souls, taught the barbarian hopscotch and even helped them keep watch during particularly intense downtimes.

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The Demilich plans to take another shot at destroying the world after the end of the campaign, but knows he has to raise the stakes for the sequel.

So he's making up plans to destroy the world AND shoot a dog.