The only thing installed over the net is Java, and that's if you don't already have it. Given that LimeWire requires the internet to work at all, I think it's a fairly safe bet that people downloading LimeWire will have an internet connection to install Java.

Regardless, if it can't connect to the internet to download Java (if it needs it), installation will proceed just fine, and when you go to start LimeWire it'll remind you that you need to install Java.