If you are using LW 5, turn on the option to auto transfer songs to iTunes. If using LW 4, then see How to transfer music to my iPod (& iTunes) {click on link}. This does in fact mention about LW 5's option.

That LW playlist you see is simply a playlist. The songs themselves are not in iTunes music library. It is purely intended for playing your new downloads. The LW Library icon you see is intended for sharing on a LAN network such as to a fellow family member for playing only. Both those playlists can only be played, not burnt or transfered to iPod.