I downloaded music from my Google Drive on my LG G4. The songs are in the Downloads folder and I can play them. I cannot figure out how to move them to my music library. I am using Music version 4.70.9.
Welcome to Android Central! Are you talking about the stock Music app from LG, or the Google Play Music app?
Try using a file manager app and copying the music from the Download directory to the Music directory. It's ideal to maintain the standard folder hierarchy of Artist>Album>Song.