Same way as when deleting about any application on a Mac: Drag the Limewire app from Application folder to the trash, and also the Limewire preference file (users>your name>library>preferences>Limewire).
Empty Trash.
Exceptions to that rule: Applications that come with an installer application (such as Microsoft apps). Those should come with a supplied uninstaller. But I doubt Limewire would require an installer/uninstaller. If it's drag and drop install to put the app to Applications, it's drag and drop to Trash it too.