I had exactly the same problem... I checked that cryptic FAQ...

This is what I did which solved the problem:

Just append the following to "/etc/profile"

PATH=$PATH:<path to jre bin dir>

I installed the Java Runtime Environment into /usr/lib/, so in my case the line would read:

PATH=$PATH:/usr/lib/jre1.3.1_02/bin

Then I restarted the system. Check if it worked by typing:

java -version

If you see a proper JRE version output, you're set to start the LimeWire installer.