Try uninstall your current version of Java and reinstall JRE using the offline installer
http://java.sun.com/javase/downloads/index.jsp
After that, reinstall LW using the offline installer
http://www.limewire.com/english/content/download.shtml
You could also try deleting the limewire pref folder. Insrtuctions here(points 2 and 3):
Fixes for Limewire when LW isn't operating as it should!.