Excuse my english but I'm a frenchie newbie in Linux World.
This message is for all newbies like me.
To install LimeWire on my Mandrake I downloaded j2re-1.4.1_01 on Sun web site:

On a terminal type(with su rights):
./j2re-1_4_1_01-linux-i586-rpm.bin

Accept the agreement to obtain a rpm package.
Install this rpm.

If kaffe (A java virtual monitor) is installed, remove this package.

If you try to install LimeWire now, you obtain a message error: no java virtual monitor installed (or something like this). Don't panic

In your home directory, show hidden files and edit your ".bash profile", type with Kedit:
PATH=$PATH:/usr/java/j2re1.4.1_01/bin

In your terminal, type:
source .bash_profile

Now type(in your LimeWireLinux.bin directory: for me ~/Documents/téléchargements):
./LimeWireLinux.bin

Et voilà, LimeWire installer is launched and you could install this program.

It is not the better way to install LimeWire but it works with my Mandrake9