The Faith aren’t really Lovecraftian. They’re pretty straightforward Fantasy Catholicism.
There are Lovecraftian religions in ASOIAF:
- the Faith of the Drowned God has a lot of Cthuloid undertones.
- In ADWD you have the Cult of Starry Wisdom, which is a straight lift from Lovecraft. In “The Haunter of the Dark,” they’re a cult of Nyarlathotep worshippers based in Providence, Rhode Island.
- The Black Goat of Qohor is pretty close to Lovecraft’s “Black Goat of the Woods with a Thousand Young” which shows up in “The Whisperer In Darkness.”