Install this version of Java. Use the JRE offline installer & remove your current version(s) of Java before you install this one.
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11

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

Lastly, reinstall LW & make sure to use the offline installer (when you click to download LW & the download box pops up, cancel it...then you'll see the option to download the offline installer).