1) LimeWire is pretty pathetic in my opinion. Before messing with Java, you might want to check on some of the other P2P options.
2) If you DO want to install Java, go back to Sun and download the SDK. It comes as a .bin file. You have to make that file executable (chmod +x filename.bin) and then execute the file (./filename.bin). However, this just installs Java, it doesn't tell the system where Java is so if you try to install LimeWire you will just get a bunch of error messages about not being able to find a JRE. To make Java generally avaiable, I like to edit my /etc/profile file. I add the Java bin directory to the PATH statment and I set up a JAVA_HOME environment variable pointing to the Java directory. You can also do the same thing in your .bash_profile, but then Java isn't available to all users.