Providing that the songs are in a format that iTunes supports - they should transfer to iTunes.

It makes it really hard for us to help when we're not given any info - we don't even know which version of LW you're using. Or which version of iTunes.

The 'shared LW tunes' is just a playlist. Those songs haven't been added to the iTunes library. It's just so that people can play their LW downoads through iTunes, if they want to. That playlist only shows when LW is open. And you can't transfer files from that playlist onto an iPod.

What happens when you go (in iTunes) File > Add file to library. Then browse your computer to find LW's saved folder & add songs from there?