The in-game part of league of legends is a different window, separate from the lobby. If the game is running fullscreen, you need to use game capture on it while it is in-game, or, alternatively, set league of legends to borderless mode, and use window capture on it.
For league of legends, as usual I would recommend using two scenes, one for lobby that uses window capture on the lobby, and one for in-game, which uses either game capture or window capture on the in-game window, and switch between them as necessary, with the automatic scene switcher plugin in the plugin forums, or by using scene hotkeys.