A playlist doesn't contain the music files themselves...just points to where they are (or were) on your computer. If the files have been deleted, the playlist won't play.

You could always try a file recovery tool. Some people have had good results with Restoration.
Deleting files from LW library - Don't!! File recovery advice

LW's Beta version will move files to the recycle bin if they're accidentally deleted
If you're interested in trying the Beta, you can download it from the LW site, or from your personal download link if you're using Pro.