1905 isn't too bad. If he avoids the nervous breakdown he suffered in 1908, he'd probably be able to graduate with a high school diploma. Lovecraft intended to use that diploma to go to Brown and become an astronomer, though; he turned to writing after high school, starting with poetry. If he's at Brown, I imagine he ends up dropping his original goal of becoming an astronomer; he's likely to get frustrated with the advanced math (as he did in high school in OTL). Not sure what he'd go for, or if he'd just drop out; for the purposes of this scenario, he should probably go for political science, so that he gets interested in politics, rather than writing.
Potentially, he could've volunteered for the military around 1917; a bit of war heroics would do him well. Alternatively, or just after the war, he could've gotten involved in Rhode Island politics, which would've meant Republicanism. He ended up being a
New Deal Democrat, but only after the Depression started; before then, he was likely a solid Republican. As long as he finds solid employment, his racism would be moderated, if
Houellebecq's thesis is right.
If he turned on the GOP in '32 and ran as the Democratic candidate for Governor of Rhode Island, he'd likely have won -
Theodore Green did in OTL. He could've followed Green's political career and become a US Senator in '36, and his health would probably have been much better, so I imagine he could've lived into the '60s (as Green did, despite having been born in 1867).
This Lovecraft is pretty much unrecognizable, but it doesn't seem implausible to me, particularly given how early the PoD is in his life.