Uninstall your current version of Java, then reinstall this earlier version. Use the JRE (Java Runtime Environment) offline installer.
Java SE Downloads - Previous Release - JDK 5

Now delete LW's preferences folder when LW's properly closed. See point 3 below (also point 2 if you've used much older versions of LW in the past...there could be a folder in the old location too).
Fixes for LimeWire

If still no joy, reinstall LW. Make sure to use the offline installer (not the recommended one). Installing again will automatically remove the previous version
LimeWire: The Official Site for the Fastest File Sharing Program on the Planet