do you have the JRE installed? To see if you do, bring up an xterm and and type 'java -version' and see what the results are. If it gives you a version number then you are good to go and LimeWire should work and the fix is beyond me...
However if it says 'Command java not found' then you don't jave the JRE installed, or your path environment variable set properly. Download the JRE (Java Runtime Environment) from www.javasoft.com
install it for your distro, and note the location where it is installed to. You will need to edit your .bashrc file with a line similar to this export PATH=/path/to/your/java/bin/directory:$PATH and log out and log back in and run the command java -version and see if it gives you the version number. My .bashrc entry looks like this:
I downloaded the JRE with the Forte for Java Community edition IDE so your path may be different. Good Luck,