1. Go to LW's menu bar, Tools>Options>iTunes>Sharing & make sure it's labelled & enabled.
2. Open iTunes & go to menu bar, Edit > Preferences > Sharing & make sure options are enabled.
Close & re-open both programs.
If still no good, go back to LW's iTunes sharing option, disable it, press apply, then re-apply. Then open iTunes. Last resort is deleting your LW Preferences folder whilst LW is
closed; instructions here:
Point #2 & 3 in Fixes for Limewire (sample image included at bottom of page.) But beware because you will need to reset all your options for LW next time you open it & so make a note of them before you do this.
BTW remember the LW Playlist in iTunes is simply a playlist that reflects the song files in the LW download folder. If you wish them to be a part of iTunes Music library then you need to add them; see how to do that here
How to transfer music to my iPod (& iTunes)