LimeWire is a multi-platform Gnutella client with nice features like auto-connect, groups, browse host, multiple search, upload throttling, connection quality control, library management and sophisticated filtering. It is built for the both the novice and power user.
Preparing your system
First you need to install java using this instructions
Open Synaptic Package Manager from System>Administration and then click on other software and add the following line
deb http://archive.canonical.com/ lucid partner
and then close the Repositories window. Now, Reload and then close Synaptic.
Now you need to install sun-java6-jre packages
Once you installed java you need to download .deb package from here once you have LimeWireLinux.deb packe install by double clicking on it.