HP Lovecraft is, in a sense, a modernist writer. Not stylistically, but philosophically: the horror is senseless, unknowable, beyond our ken. It's not ghosts from beyond the grave, devils, and curses. It's alien gods with strange motives, indifferent to human suffering. In this sense Lovecraft is a classic post-WWI writer. On the one hand, the message is that what was once certain no longer is. On the other, the message is that you can create something completely new. No more devils: let's talk Cthulhu.
This is what makes Lovecraft particularly interesting, of course, but what's a strength can just as much be a weakness. What you gain in otherworldly, alienating horror, you lose in cultural resonance. You really notice this when you read MR James, who was probably the last great pre-modern horror writer - in the sense of having Victorian rather than modernist sensibilities. James's universe is one where things make a kind of sense, even though he was expert in keeping things hidden. The ghosts, spirits, demons who his protagonists encounter are products of Christianity; it's a vicious, vengeful, Old Testament Christianity, where sins are punished rather than forgiven, and it's a Christianity which comes more from the Apocrypha (The Testament of Solomon, Knights Templar, medieval Jewish magic) than from the Bible, but it's still a universe people from the Western world are familiar with. It's in many ways a quid pro quo universe - you get what's coming to you - but more importantly it's one that's horribly familiar, especially if you have had a church upbringing. Words like Baphomet, Satan, King Solomon, hell, the afterlife, altar, pew, prayer book, etc., have meanings to us which extend beyond the immediate story or what the writer can conjur up, and reach into our shared Judeo-Christian cultural past. This gives them a sense of weight, a sense of meaning, that made-up words like Hastur do not.
This capacity for cultural resonance is underrated. You don't have to be religious to appreciate that certain shared myths, stories and artefacts can take on a sense or feeling of the numinous, despite your own agnosticism: they get it not from the fact that they're true, or genuinely 'spiritual', but from something deeper - they've been around a long time, thousands of years in some cases, and when something is around a long time, it tends to grow roots. The Testament of Solomon is spellbinding because these are stories which have their roots in extreme antiquity, and something that old can't help but feel significant. And if you really object to accepting that is true of Judeo-Christian religions, it is just as much true of Greek myth, or the Epic of Gilgamesh, which also have that quality of numinousness arising from their great age and survival, and the meanings and connotations that inevitably accrue whenever something is truly old.