Yeah, Nietzsche (from my very lay understanding) would certainly count as a proto-postmodernist, or early anti-modernist, or at the very least a huge influence on the postmodernists. Nietzsche's influence is all over HPL, to the extent that I think one of the reasons the middle-aged Lovecraft disparaged the writing he'd done in his 20s and early 30s is that he saw it as the work of a barely post-adolescent Nietzsche fanboy. But the influence is there even in his later, better work - there's that great line in TCoC
about mankind becoming, like the Great Old Ones, "wild and free and beyond good and evil
" - couldn't really be any more explicit, could it?
In fact that whole passage is very reminiscent of the credo "Nothing is true, everything is permitted" of OG hashshashin
Hassan-i-Sabbah (another favourite of Burroughs), later quoted and extended by Aliester Crowley:
Nothing is true, everything is permitted: Do What Thou Wilt shall be the whole of the Law
As systems of ethics goes, that's pretty damn postmodern!
There's a great essay by a guy call Sandro Fossemo called 'Cosmic terror from Poe to Lovecraft', which touches extensively on the Nietzsche-Lovcraft connection. Annoyingly I can't find it online, seems to have been taken down from the site that was hosting it. I'll post it here if I can find it somewhere else. There's a great line in it that goes "Poe sinks in[to] the soul to knock down external reality, Lovecraft on the contrary sinks in[to] the cosmos to demolish inner reality", which I thought very apt.
If you're into the whole critical-theory/deconstruction thing (not that I am, as a rule) I think you'd find Cyclonopedia
very interesting - a lot of people have looked at that thread I started about it but no-one has replied yet. It's pretty fucking recherché
but I found it fascinating. It really does come across as the work of a modern-day polymath 'mad Arab' (well, Persian in this case, but who's counting?).