Here's how I got my desktop link to work. I edited the runlime.sh file so that it looked something like the following.

#!/bin/bash
cd /home/home/LimeWire
J2SE_PREEMPTCLOSE=1; export J2SE_PREEMPTCLOSE
java -jar RunLime.jar

(of course, your LimeWire installation will probably be in a different directory)

After this change, making a link to this file should work.