Have you tried uninstalling LimeWire and Java by going to Start/Control Panel/Programs and Features and uninstalling all versions of Java and LimeWire. Then re installing Java first using the offline installer then LimeWire using the offline installer. You can get Java at the link below use
Java Runtime Environment (JRE) 6. Try using the beta version of LimeWire 4.13.2 it has been working for me with no problems. You can get it at the second link.
http://java.sun.com/javase/downloads/index.jsp http://www.limewire.com/english/content/download.shtml