m3u is a playlist file which is simply a reference to the location of the file. So if you move or delete the original file your playlist won't work. Are you using WMP? wmp is simply a reference player & it doesn't actually import the songs but creates a playlist or imports playlists. The LW playlist function is not intended for movies. You should move the files out of the LW downld folder before adding to wmp.

If you're using iTunes then you'll need to add the songs to iTunes music library. You need to do this using iTunes; see: iTunes & iPod importing (click on link) Once the songs are added to iTunes Music library you can then delete the original copies.