Try doing a Safe Boot & repairing permissions. ie: Hold down Shift key whilst the comp's starting until you see the message 'Safe Rebooting'. Then once started up, go to Utilities folder, open Disk Utility & repair permissions. Then reboot.

If LW still doesn't open, delete the LW preferences which is found here: /Users/your_username/Library/Preferences/LimeWire

Depending on which version of LW you have, if you have 4.10 then use the Find/Search to search for limewire or application data. You may need to search using the option for show both visible & invisible items. If you find it, trash the limewire file/folder.