There's a bug in LW that conflicts with OSX. Just check "disable ultrapeer" in your preferences (Speed), as david said, and:

You should also set up your firewall to allow gnutella (OSX->System Preferences->Internet and Network->Sharing->Firewall->New->Port Name->Gnutella/Limewire (6346).

Then you can have fun figuring out the many other problems that are likely to crop up, and David pointed out.

Cheers.