For some people some versions do not work or work as well as other versions. Try steps 5 & 6 here:
Fixes for Limewire (click on blue link).
If that does not work, then try this:
http://www.gnutellaforums.com/333278-post2.html but instead try this version of Java
Archive: Download Java Platform Standard Edition (Java SE) 6u5 & use your installer you downloaded previously for LW. Sometimes one version of Java works better for LW on some people's systems.