Remove your current version of Java & reinstall the JRE using the offline installer here
http://java.sun.com/javase/downloads/index.jsp

Now try reinstalling LW using it's offline installer, it should uninstall the old version before reinstalling the new one
http://www.limewire.com/english/content/download.shtml

If that doesn't work, you might have to delete all LW files manually & then reinstall the new LW version.

See how that goes & let us know if you're still stuck