Ooooph; where to begin? Had you picked two of the more modern writers, it might have been easier; but King and Lovecraft are, in most ways, about as far apart as one can get. True, both wrote horror tales, but King is very modern, HPL was very much influenced by older literary models, though his philosophical outlook ("cosmic indifferrentism", as it's been called) was very modern indeed.
For me, it is difficult to see areas of similarity; King largely deals with traditional tropes, Lovecraft tended to avoid such, or to give them entirely new spins (though those have now become, themselves, stereotyped), as with the ghoul-changeling theme, or the ghost/avatar, or the vampire as seen in "The Shunned House". Also, King is much more violent and given to gore; Lovecraft was almost entirely about atmosphere and implication; what violence or gore there is in his stories is largely off-stage or distanced, where King places the reader right in the middle of it.
Perhaps there is one slight similarity, in that King does allow for the universe to be a place wherein human beings are at the whims of chance or laws they cannot understand; though I must say I feel Lovecraft conveyed that much more powerfully; both writers, however, had no inclination to soften the impact of this on their most sympathetic characters. So perhaps that could be one point on which to compare them.
Mostly, however, I think it would be contrasting their styles, approaches, philosophies, etc., even though King has written some Lovecraftian pastiches (the short stories "Jerusalem's Lot", "Crouch End", "Gramma", the novella "The Mist" all having Lovecraftian elements, for instance).
I have a question: How long do you have to do this? There are quite a few good books on Lovecraft out there, though most are not carried by bookstores; the best biography is S. T. Joshi's H. P. Lovecraft: A Life, which far supersedes the earlier biography by L. Sprague de Camp; Donald R. Burleson's H. P. Lovecraft: A Critical Study is a good brief examination of his life and work, rich in ideas that may give you some good directions in which to go. There have been several books on King, but I'm not really familiar with any of them, so can't recommend anything there. Perhaps someone else here can do so?
At any rate, welcome to the Chronicles, and I hope some of this helps. If you'd like more information, please feel free to PM me, or to ask for further information in this thread. Good luck!
