The LimeWire Tunes that you see is just a playlist & the files aren't actually in the iTunes library. You'll have to add files to the iTunes library to be able to transfer them to your iPod
You'll need to add files to the iTunes library from LW's saved folder. Tools > options > saving will show you the location. Or, go to LW's library & highlight a file & then click Explore...your saved folder will open! Read through the thread below for more info about adding songs to iTunes & iPod.
Transferring music to iPod & iTunes