It seems to me that the biggest thing about DF which makes me feel helpless is when my dwarves do stuff and I can't do anything about it. Despite everything I have at my disposal, that Forgotten Beast is still shredding my dwarves left and right. There's a loyalty cascade or a tantrum spiral going and my dwarves WON'T LISTEN TO ME. I think you might be able to capture some of the Lovecraftian atmosphere by making the player feel powerless IN SPITE of what they can do rather then powerless because they can do nothing. In Masterwork, at some point, there was a cult of the Carp God that could get going in your fortress. You'd start receiving strange messages about your dwarves discovering mutilated corpses in the refuse pile and ritual circles being drawn in blood in random places. And then one of your workers would suddenly and apparently randomly turn into a horrid fishy abomination and go on a rampage until it was finally brought down. THAT is how you can do Lovecraft stuff in DF. The thing which made the Cult of the Carp God so effective is that its bundled with so much other stuff. The average player playing Masterwork has no idea that the Cult of the Carp God is even IN the mod because its so bloated with features. So it comes as a disturbing surprise when normal dwarves start doing creepy things and turning into monstrous fishmen. A dedicated Lovecraft mod wouldn't quite be able to capture that, because the entire porpoise of the mod is to do that kind of stuff and anyone who downloaded it would be expecting it. IMHO, the best way to use a Lovecraft mod would be to use it in a succession fort WITHOUT TELLING ANYONE ELSE.
Although you could totally just add in Lovecraft stuff too. Some of his stuff was sorta sci-fi and you could do some interesting stuff with the Elder Ones and the Great Race having ancient ruins buried in the caverns from a gameplay point of view. Stealth shoggoths, for one. I know there's SOME way to modify death messages, possibly via DFhack, so you might be able to have it work something like this:
1: Opens up caverns to get water on glacier and trawl for ancient artifacts
2: Stealth shoggoths enter the fort without anyone knowing
3: Dwarves start getting their heads sucked off
4: Shenanigans ensue
Stealthing creatures are another one of those things beyond the player's reach. You literally have no in-game clue what the hell's going on with them. Once again using Masterwork as an example, I spent maybe a year in one fort with a stealthing necromancer reanimating legions of the dead. Eventually, I managed to kill him by using magma to initiate a fiery holocaust on the surface, torching a scattered group of migrants in the process. But, for that year, I was extremely paranoid, afraid the necromancer would get into my fort via my well or something and start reanimating all the corpses in my refuse stockpile while still being invisible and unkillable.