Have you tried Java 1.6 (offline JRE installer)? You'll have to remove any other Java versions before install.
http://java.sun.com/javase/downloads/index.jsp

And you could also try the LW 4.13.0 Beta...it's made a difference for some people.
http://www.limewire.com/english/content/download.shtml

Do things freeze when you're downloading as well as searching?
Reduce the drag caused by LW