Go to Add/Remove control panel & remove all versions of Java. They might be called JRE or JSD or JDK or JSE/JME. Then install Java 1.6 Beta http://java.sun.com/javase/6/download.jsp JRE "Offline" version which is a 15.72 MB download.

Also delete the LW prefs folder if you have any; see Point #2 & 3 in Fixes for Limewire (sample image included at bottom of page.) You might also consider trying step 5 in that link.
BTW it's best & safest to use the "Offline" LW installer.