Justin Vernon, the singer, has lyrics written by Indigo Girls tattooed on his chest. So that's one inspiration. Find out some more like Elliott Smith and Tom Petty, in this Perfect by Atze de Vrieze.
Apart from visuals, David Lynch was also sound; music often felt like a character in his films and series. Songs lost their innocence through the disturbing scenes in which they shone, and overtly nostalgic music suddenly seemed to come from another world.