Normally if you add a song it goes to your main iTunes Library. If you already have the identical song already in the library, then iTunes won't allow you to add it. If you want the original file already in the library to be added to other playlists then simply add it/drag it from the library to the new playlist. You only need a single copy in your iTunes Library. It is a song file you're adding isn't it, & not a playlist to iTunes. You can't have more than one copy of an identical file in the iTunes library if it "is" identical in name & bit rate, etc.

Don't get confused with the LW playlist within iTunes. That just refers to songs in your LW downld folder. See How to transfer music to my iPod (& iTunes)

If I'm misunderstanding your problem then please supply more details.