It sounds like you're a windows user not a mac user. To properly add music to iTunes follow the directions here: Importing songs to iPod & iTunes

So you thought the LW playlist within iTunes meant the songs were actually within iTunes Music Library. No, you need to add them yourself.

You've created playlists within LW & imported those to iTunes but haven't consolidated the library.

Always look in the main iTunes library list to ensure the files have been properly imported.

If you're missing any songs from any of your playlists or they're not where they were originally then the playlists probably won't work. It might be better if you create new ones from the files you've managed to recover. PC Recovery is apparently very effective & a good utility considering it's free. But user reviews suggested it can be a pain to use. And perhaps recover the files bit by bit. Recover them to a different HDD or partition or storage device other than the one they were stored on otherwise you may overwrite the skeletons of the remaining erased files.