Regarding your message "No Virtual Machine found," I have been through this same frustration on three seperate occassions--3 different versions of RH.

The following does it for me every time:
$ export JAVA_HOME=/usr/bin/java/j2re
$ export PATH=$PATH:/usr/bin/java/j2re/bin
$ sh LimeWireLinux.bin

Obviously, you will need to adjust the paths above per the location of your java install.

Good luck!
Thomas