Reinstall Java. Use the JRE offline installer & remove your current Java version before installing the new one.
Java SE Downloads

Now reinstall LW & make sure to use the offline installer (not the recommended one).
LimeWire: The Official Site for the Fastest File Sharing Program on the Planet

If that doesn't help, delete LW's preferences folder. See point 3 below (also point 2 if you've used much older versions of LW in the past). This will kill all of your settings within options, you'll have to go back through & reset things afterwards.
Fixes for LimeWire