I'm really surprised that the Mi-go don't show up in any capacity. They might be a little immediately identifiable as a lovecraft property, but there's no rule against having some vaguely recognizable flying fungus beast that removes peoples' brains for kicks, is there?
Lovecraft also wrote (or at least published) earlier than JRRT. Some of his work is old enough to not fall under the various retroactive copyright extensions. It's not clear whether others are covered due to lack of renewal.
More importantly he encouraged other writers to refer to his mythos and there have been many Cthuloid stories written since his death. Many by hacks, but some quite good. Without that it's likely he would be all but forgotten.
It was a different world back in the twenties. He sold to the pulp magazine market, got paid by the word and had little chance of getting royalties or anything like that.
A lot of it was just references to the same fictional occult tomes (like the Necronomicon). And that helped both parties by making them seem more real.