INSPIRATION IN MUSIC
H.P. Lovecraft's creations inspired plenty of songs present in today's popular culture, even ones from well-known bands such as Metallica, Black Sabbath or Blue Öyster Cult. It doesn't seem unusual that those bands found some reference in Lovecraftian Horror, the themes of the unknown Elder Gods hiding right behind what is comprehensible for normal human beings or the eldritch horrors ready to bring doom over the earth. Below you can find some examples of music.
METAL MUSIC
Metallica and Black Sabbath are probably the most known metal bands which have songs inspired or related to Cthulhu, Metallica's "The Call of Ktulu" and "The Thing That Should Not Be" are probably most evident ones, although Black Sabbath's "Behind the Wall of Sleep" is a strong contender. Another one being a band Shub-Niggurath using one of the Elder Gods as their name and referencing other ones plenty of times in their music.
ROCK MUSIC
Blue Öyster Cult is a rock band that should be recognizable by most, their song "The Old Gods Return" references the Elder Gods of Lovecraft's universe who will "[...] sweep our cities back to Hell". Other less known bands include Blind Idiot God which name references Azathoth one of the beings from Cthulhu Mythos, or an English band Caravan and their song "C'thlu Thlu".
ELECTRONIC MUSIC
Lovecraft is a reference even in this kind of music, used by artists such as Deadmau5 in his songs "Cthulhu Sleeps" and "Rlyehs Lament", it's interesting to see how seemingly unfitting things found a way to be combined into one. Another artists worth mentioning are Ida Engberg and Adam Beyer who released an album in 2012 called "The Color out of Space" which includes a song with the same title as well as one titled "Lovecraft" - I don't think you can get a more direct reference than that.