HP Lovecraft was building on earlier work by Ambrose Bierce and Robert W. Chambers.
Lovecraft created the Necronomicon, as part of the Cthulhu mythos, but he allowed his friends to play in his universe. More than that, Lovecraft worked as a copyeditor for pulp magazines during the 'twenties, and he would insert Cthulhu material into stories by other people (without their permission--such was the happy, carefree life of the freelance writer back in those days). The mythos has since taken over an entire sub-branch of horror (I've used it myself--
Land of Mist and Snow and "
Philologos"). Various books purporting to be the Necronomicon have been published.
The Necronomicon first appeared in 1922, (and Lovecraft himself died 70 years ago in 1938) putting it well into the public domain.
You can use it, but if you do you should be aware that your readers will expect that your book is part of the Cthulhu mythos and will have certain other expectations as well. (Including, but not limited to, Arkham Asylum (yes, the current incarnation of Batman is located in the Cthulhu mythos), Miskatonic University, and the seafood festival at Innsmouth.) If you are going to use the Necronomicon, know what it is supposed to be, and use it in a manner that is not inconsistent with others. This will keep your readers from throwing your book across the room.
(At one point in my life I owned a "It's The Great Old Ones, Charlie Brown!" tee shirt.)
(In "Philologos," which was written as my entry in one of this thread's Christmas Challenges (and subsequently published by F&SF, thanks very much), our hero, William R. Sharps (the "R" stands for Romeo, but he doesn't
ever tell anyone that) winds up in Castle Dracula (which is never called by name in the story ... but long-time readers of fantastic literature will instantly recognize it), but nothing there fazes him -- for he went through Finals Week
eight times at Miskatonic U, after which facing the undead and unholy religions is ... well, those unholy undead didn't know what hit 'em.)