Are you sure you're capturing the LoL Game and not the client window? Because the client can't be captured with Game capture, since it's not a DirectX/OpenGL game, just a window.
The best way to stream LoL is to set up 2 scenes. First, keep Aero enabled. Then, in the first scene, have a Window Capture of the LoL client, and in the second scene, have a Game Capture of the actual LoL game (or Window capture if the game is in Windowed or Borderless mode). Then use the Simple Scene Switcher to automatically swap between them:
viewtopic.php?f=11&t=1785 Avoid Monitor capture altogether.