Yes! Lovecraft read fairly deeply in weird fiction, especially during the mid-to-late 1920s when he was researching his essay Supernatural Horror in Literature, which he would continue to expand and revise throughout his life.
Lovecraft's earliest influences include Lord Dunsany, who began producing fantasy fiction with The Gods of Pegāna (1905), which introduced the idea of an "artificial mythology" which Lovecraft would develop in his own fiction, for example when he came up with the idea of Cthulhu. Edgar Allan Poe was another major stylistic influence, to the point that Lovecraft once declared:
There are my 'Poe' pieces and my 'Dunsany pieces'—but alas—where are my Lovecraft pieces?
A third and very critical influence was Arthur Machen, who had gained notoriety in the 1890s for works like The Great God Pan, which Lovecraft would go on to reference in "The Dunwich Horror."
Later in life, Lovecraft would thrill to The King in Yellow (1895) by Robert W. Chambers, which he would incorporate into his The History of the Necronomicon, and the weird works of William Hope Hodgson, a major British influence of turn-of-the-century weird fiction whom Lovecraft did not read until relatively later in life.
Chambers and Machen were both retroactively borrowed into Lovecraft's Mythos, but they were representative of a tradition of weird fiction that was outside the run-of-the-mill ghost or werewolf or vampire story; in his letters Lovecraft would praise Guy de Maupassant's "The Horla" (1887), Ambrose Bierce's "The Damned Thing" (1893), and Algernon Blackwood's "The Willows" (1907) very highly, and considered Blackwood, Machen, and M. J. James as contemporary masters of the weird tale.
While none of these writers was explicitly writing to Lovecraft's definition of cosmic horror, he took them all as literary forebears and their influence (except Hodgson, but only because he was discovered so late) can be definitely seen in his work. On the non-fiction side of things, Lovecraft also took great inspiration from Margaret Murray's The Witch-Cult in Western Europe (1921) which, while erroneous, he combined with the subdued occultism of Arthur Machen and developed into a quite extensive theory, providing a background for stories such as "The Dreams in the Witch House."
Lovecraft had influence from living authors as well - he borrowed directly from Clark Ashton Smith, Robert E. Howard, August Derleth, Robert Bloch and others, and encouraged them to borrow from his work as well.
I read somewhere that Alister Crowley had some influence on him. I think it said he dated Crowley's ex and her stories of a book that Crowley kept locked away was part of the influence for the necronomicon. Is there any truth to this?