Showing Someone else's Limewire music in my ITunes
 

My ITunes shows someone else's Limewire tunes. This was before I had re-logged into Limewire. Then I logged into Limewire and it shows both my Limewire Tunes and this other individuals...?

Any Ideas how and why that is?

It means you're on a network & you have iTunes options set to allow sharing. It means you can play but not copy other people's playlists on your iTunes. It's related to daap & bonjour
So I presume your computer is on a lan or wan right?
As for your LW playlist in iTunes, it's enabled or disabled by going to LW's menu bar, Tools>Options>iTunes>Sharing
iTunes sharing option is controlled by going to iTunes menu bar >Edit>Preferences>Sharing