You actually need to install limewire with java. I used the newer version of java 1.3.1 which is kinda big (14.1 Mb) if you have a 56k. You can get it at http://java.sun.com/j2se/1.3/download-linux.html.

You will also need the LimeWireOther.zip file.

Then as someone else said,

Install jre 1.3.1.
Download LimeWireOther.zip file.
From within xinit or gnome open xterm, change to the directory you downloaded LimeWireOther.zip to, and type:
"sh" (with out quotes), hit enter.
Type: "/usr/java/jre1.3.1/bin/java -cp LimeWireOther.zip install" (with out quotes), hit enter.

I've found that it's best to type something similar to the following:
/usr/java/jre1.3.1/bin/java -cp /(Directory where you want it)/LimeWireOther.zip install

The installer loads and just follow on screen instructions.

As with most of my applications, this one decided to fight me, and I had to back out one directory (/..) to get it to put the files where I want them to.

This method works for root, as I haven't sorted out the connect problem that many others seem to be having. But something is better than nothing.