A suggested, steps 1,2,3 & 5 here
Fixes for Limewire. That will mean using your add/remove control panel to remove all previous Java versions before reinstalling. For some people, even a reboot after doing all these steps may help (before trying LW again.) Also reinstall LW using the "Offline" LW installer from here
http://www.limewire.com/english/content/download.shtml