If you do not have java installed then you need to go to
http://java.sun.com and download the appropriate version for your system. After you have java installed just make a symlink to the java executable with the following command executed as root
ln -s /usr/java/j2re1.4.1_01/bin/java /usr/bin/java adjusting appropriately for the proper location of your java executable. LimeWire will then find java and run with no problems.