Lovecraftian horror doesn't work well in games (Or movies for that matter) because it's core principle is the fear of the unknown. That of our insignificance in a greater universe, of the sheer magnitude to which we are outmatched.
To that end it's rarely well done in either games OR movies simply because both are visual storytelling medium, and the instant you *show* a Lovecraftian terror it's not really Lovecraftian anymore. People think 'oooh, goopy weird tentacle monster = Lovecraft' and they're wrong. Probably some of his most compelling horror such as Colour Out of Space has no real 'alien' or monster, not one that we can understand anyway.
Still if you want its best presentation in games Dark Corners of the Earth as mentioned above is quite good, and Eternal Darkness is another. Oddly enough Mass Effect 1 as well, but only 1. Your initial encounter with the Reapers is very Lovecraftian in nature; a creature of unimaginable size and scope completely foreign to human comprehension working for reasons we cannot fathom.
Unfortunately in the later ME games that Lovecraftian vibe was dismissed, but for the first game at least it was definitely present.