I got it guys! I just had to find the post that helped me when I went through this the last time I set up LimeWire. This works for me EVERY TIME so I hope it can help someone else who is feeling frustrated out there.

$ export JAVA_HOME=/usr/bin/java/j2re
$ export PATH=$PATH:/usr/bin/java/j2re/bin
$ sh LimeWireLinux.bin

The above has gotten me thru the "No Virtual Machine" message three times now.

Kind regards,
Thomas