Do you have Alcohol software installed? Have a look at this thread: LW starts then close, log: resolve_virtual_call

If that doesn't help, which version of Java are you using? Some people have had problems with the latest Java updates. Try this older version.
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11
Download the JRE offline installer & remove any other Java versions before installing this one.

And 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 change 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.