Forget about the "your name's LimeWire Tunes" within iTunes...that's just a playlist & so you won't be able to add to the iTunes library (or to your iPod) from there You'll need to find your LW saved folder. Go to your LW library, click on a music file & then click Explore...your saved folder will open. This is where you have to add from, when adding to the iTunes library!

There's lots more info here.
Transferring music to iPod & iTunes