Greetings. An RPM for LimeWire 4.4.1 is available for testing at
http://www.limewire.org/LimeWire-free-4.4.1-0.i386.rpm
It is tested to work on Fedora Core 3 and requires that you already have the Java Runtime Environment properly installed. To install LimeWire become root and type:
rpm -i LimeWire-free-4.4.1-0.i386.rpm
If that is successful, you should be able to type "limewire" in your terminal and that will launch limewire. On some systems there will also be an entry somewhere the start menu (On fedora it is in the "Internet" category).
Please give it a try and let us know how you like it.