This is exactly why I usually say it means “Something’s wrong” instead of “I want something” because the cat is perfectly capable of occupying un-pillowed laps, it just chooses not to.

I suppose in that respect, it does mean “I yearn!” but I’ve taken it to mean “Something’s wrong!”, with the nuance being that he’ll want his food bowl filled even if he’s not hungry or me on the couch even if he doesn’t immediately want a lap.