Client will not notify me when it's my turn to pick/ban in queue

I log into the game. I am in champion selection. I see that it's not going to be my turn to do anything for like 2 minutes, so I open another window and do something else. Note: I don't minimize the LoL application. My turn comes up, and LoL does not notify me.

And look, I love the fact this game is free. I know this is a first world problem. But, can we please have the application's icon flash or something? I mean, there is no warning.