There is, actually, a recently published book presenting itself as THE Necronomicon. I looked it over at the library a few months back, and couldn't tell whether the author and publisher were trying to pull something over on that part of the reading public which is drawn to the occult, or it was an elaborate homage to Lovecraft. I probably should have brought it home and compared the contents with some of the Lovecraft stories I have, but the parts I read at the library just looked like magic spells invented by a person with some knowledge of the history of magic and a particularly unpleasant mind, and I didn't.
Clark Ashton Smith was but one of many writers who set stories in Lovecraft's Cthulhu "universe". "The Return of the Sorcerer" was one, and "Ubbo-Sathla" is another. (I have both in a battered old book -- of thoroughly mundane antecedents, alas, and mere paper covers --Tales of the Cthulhu Mythos, Volume One, edited by August Derleth.) I don't know the titles of any others he wrote in that setting, but there well may be others.
I'm not aware of any actual collaborations between Smith and Lovecraft, if that's what Brys means by working together.