So, leagues cant "
" with your internet, it does not work like that. Second, from your picture, I see that you have other high mb's programs open, like skype and WMP. Skype alone can take more bites to use than leagues ever will. Maybe before you start blaming Leagues, you need to look at your own computer first. Running too many programs can cause all the issues you just said. So first, check your computer. get a program called "advanced system care" to tell you how much ram/cpu you are using. If its really high, close programs down so Leagues can work properly. If this does not work, chat with your internet provider, maybe you are not getting sufficient internet speed to run Leagues. if all that does not work, then contact RIOT directly for support.
I hope this helps.