League of Legends updated their lobby and now runs on a web-based client. Web-based content cannot be captured using Game Capture.
As a workaround, you can go on Add Source > Screen Capture > Monitor Capture and select the lobby window and add the League of Legends in-game window as Game Capture on top of it.
This way, you’ll be able to record or stream the game lobby and automatically switch to the main game when you start playing.