Mmm… yeah… but I’m not sure I’d call it “collaboration,” per se.
Y’see, Lovecraft invented his own stuff, and Clark Ashton Smith invented HIS own unrelated stuff, and Robert Howard was off writing Conan stories and suchlike, right?
Now, these guys never met, but corresponded heavily by mail. If Lovecraft was alive today, he’d be the king of the email junkies.
These three guys read each others’ work in the pulps, and admired each others’ styles quite a bit, and often included homages to each other. Lovecraft in particular invited his chums to use his weird names and imaginary books, which is why the Necronomicon pops up in Smith’s stories… and “De Vermis Mysteriis” pops up in Lovecraft’s, despite the fact that Howard originated it. Oh, yeah, and at one point, in a Lovecraft story, we hear about the mad Egyptian wizard, Klarkash-Ton…
In fact, based on some of these interlinks, you could make a pretty strong case that Conan’s Hyperborea is a part of the Cthulhu Mythos!
…but they were NOT collaborations. They were simply a bunch of chums swapping ideas and having fun with each others’ creations, with permission.
After Lovecraft died, though, his unpublished stuff fell into the hands of one August Derleth, who finished several Lovecraft projects, and published them as “posthumous collaborations,” which I guess is true enough… although he finally reached a point of writing his own Mythos stuff, popping a quote from Lovecraft in there somewhere, and publishing it as A NEW WORK FROM LOVECRAFT AND DERLETH…
It’s been said that Derleth is largely responsible for the “Cthulhu Mythos” concept, in that he wrote a lot of material that unified the concepts and fleshed out the idea of the Old Ones vs. the Outer Gods, and suchlike. Lovecraft’s stories, although they had concepts in common (Cthulhu, Necronomicon, etc) were pretty much unrelated to each other.
Derleth’s critics damn him for this, saying he weakened Lovecraft’s terrifying nihilist cosmic vision by doing so, and simply turned the Mythos into a good gods vs. evil gods series, like a cosmic Cowboys and Indians saga.
Then again, without Derleth’s creation of Arkham House Publishing, it’s possible that Lovecraft would, today, be largely forgotten… so read the stuff and judge for yourself.