Update your Java to this version. Download the JRE offline installer & remove any other Java versions before you install this one.
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11

Next, 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
This will kill all of your settings within options, you'll have to go back through afterwards & reset things. If you're not sure of your settings, go through LW's tools > options & write them all down, so that you can reset things later.

Last of all, reinstall LW. If you're going to reinstall the latest version of LW (4.14.8), make sure to use the offline installer. When you click to download LW & the dialog box pops up, cancel it. You'll see the option to download the offline installer