I'm afraid you won't be able to install LimeWire without using the dreaded terminal. Download the LimeWire installer using:

wget http://www9.limewire.com/download/LimeWireLinux.bin

Make it executable using:
chmod +x ./LimeWireLinux.bin

and then execute:
./LimeWireLinux.bin

Of course you need to have Sun's Java installed, or the installer won't execute.