Go to LW's menu bar, Tools>Options>iTunes>Sharing & disable sharing options. The other way is to go to iTunes preferences, (Edit menu) & select Sharing option & disable option.

BTW Jay's Limewire Tunes is what music you have downlded & is still in your LW downld folder. This playlist could potentially be shared over a LAN/WAN such as with family or work-mates depending upon where you are. I also disabled it because it drove my partner crazy with my playlist showing up on her computer in iTunes.