Update your Java using the offline installer for the latest JRE (point 1 in the the thread below). Go to add/remove programs & remove your old Java version before installing the update.
Fixes for LimeWire
If updating Java doesn't help, try deleting LW's preferences folder (points 2 & 3) & changing compatibility (point 5).
If you need to reinstall LW, make sure to use the offline installer (not the recommended one)
http://www.limewire.com/english/content/download.shtml