Remove your version of Java & reinstall JRE using the offline installer. See point 1 below
Fixes for LimeWire
Delete the LW preferences folder, points 2 & 3 in the thread above.
If that doesn't work, reinstall LW using the offline installer (it will automatically uninstall the older version)
http://www.limewire.com/english/content/download.shtml
See how that goes