That’s the case when a parody of a thread by another poster (or the comments of other posters in such a thread). Because you are basically ridiculing other posters, it properly goes in the Pit. (It’s also why a link is required, so people know what is going on.)
Other kinds of parodies don’t need to go in the Pit. They would probably go in MPSIMS (or if a literary work could go in Cafe Society).
Just because it was a parody of Lovecraft doesn’t mean it needed to go in the Pit. I would guess it was put in the Pit because the OP was Pitting Marmite.