You can share your iTunes playlists on a LAN using DAAP if Share my Music is ticked in the iTunes Preferences. You can share your LW playlist the same way by enabling this within LW. LW Preferences>iTunes>Sharing & tick Share my Music option. If there's no name listed then you can add your own desired name. In any case sharing your LW downld list will appear in your iTunes playlist whether you're connected on a lan or not.
