You'll need to add files from LW into the iTunes library, before you can sync your iPod. The shared 'LimeWire Tunes' is just a playlist, the files aren't really in the iTunes library...that's why they won't add to your iPod

Have a look at the thread below for different ways to add files to iTunes library. If dragging & dropping straight from your LW library doesn't work (it doesn't for some people) then you'll need to find your LW saved folder & add to iTunes from that folder. Go to LW's library, highlight a file & click Explore...your saved folder will open. Add to iTunes from there.
Transferring music to iPod & iTunes

Don't worry about the blonde bubble...the readhead bubble's a scary place, too