What version of Java are you using? Some people have had this problem with Java 1.6.0_01 Try this version instead. Use the JRE offline installer & remove your current Java version before you install this one.
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11

If that doesn't help, 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.

Reinstall LW & make sure to use the offline installer. When you click to download LW & the download box pops up...cancel it. You'll see an option to download the offline installer. Take that option.
Lime Wire » Download LimeWire

Also try changing compatibility (point 5 in the 'fixes' thread).