Regarding the rules for Vampires in the OOTS world–I just remembered that Xykon himself thought that becoming a vampire was a way to “stay in the game,” which does not to me sound like your soul gets locked up and a demon takes over your body, at least normally.
I don’t know that we should put too much weight on a throw-away snark from Xykon, of course.
Well, more to the point, a lich’s body is ultimately indestructible - he needs to have one for full functionality, but whatever happens to it, he will regenerate it or if necessary grow a new one as long as his phylactery is intact.
I assume part of the ritual of lichdom is to set this up, and the rest is to make sure that this walking-corpse-soul-jar of yours is something you retain exclusive title to, so no demonic spirit can set up shop and start pulling your strings.
It has happened in our own History. Hades had little to no worship beyond a few cults, the Oracle of the Dead and some recognition at funerals. No temples to speak. In Norse mythology Hel might be in the same boat. If Google is any indicator Hel has more worshippers today than in the age of the Vikings.