Like Robert E. Howard, Fritz Leiber was a contemporary of and corresponded with Lovecraft. Also as with Howard, Leiber was greatly influenced by Lovecraft.
Leiber's first book (not short story) was published by Arkham house, the small publisher that primarily handles books related to the Cthulhu Mythos.
Legend has it that there were far more references to the "mythos" in Leiber's early stories, but that he removed them under prodding from Lovecraft who felt that Leiber's work deserved to stand fully on it's own.