You can already set up music to play while in car.
Options/Audio
then you have choices of
Music in Setup screens
Music while racing
Music during replays
Pick an ingame Channel (1, 2 or 3) - in this case, Channel basically means which radio station you want playing.
Look at bottom right of screen and you will see a button called Channels - click it, and it takes you to a screen where you can pick music and set music per channel.
Any music you want in there, save as OGG music file in your LFS data/ogg directory.
Easy enough finding mp3 to ogg converter to download.
Or if all that is too much work, play your mp3's on your pc or audio equipment in background while playing LFS.
To be honest, last thing I would want is to have to listen to other peoples music blaring from their cars while racing. I've almost given up watching youtube movies because of the awful music people use as background. Especially true for drift videos.