Someone who cares about lovecraft tell me the lore
The relationship between Yog-Sothoth and Hastur and Probably-Shub-Niggurath is actually the biggest break from the lore (such as it is) in the comic. Usually, Hastur is represented as Yog-Sothoth's offspring, but Shub-Niggurath is usually portrayed as his mate rather than his mother, when they have any particular relationship at all. Really for this comic it's all just window dressing for wacky gags anyway, though, and knowing Lovecraft doesn't add too much.
There is one more thing that I thought the comic was doing differently from the canon of the stories (The Dunwich Horror in particular), but it turns out they're following the story after all - but that's a spoiler for the next couple updates.