It kind of depends on the framerate and quality you would want to see in but generally speaking anything over 5Mbit is more than sufficient. A key thing here is that the Twitch.TV staff frowns upon anyone consistently streaming at over 3500 Kbps. So, as long as you have an Internet connection that is faster than that (LoL is a bit of a bandwidth hog, as I said, so, leave some room for it) you should be fine.
TL;DR -- 5Mbit would be just fine, 3Mbit and over will most likely be sufficient.