Hello Porsche26,
you need to set 2 different scenes for each window. One scene which captures the browser and one scene that captures the lol cient. Then in the Scene switcher you need to set the defined scene to the appropriate window.
Example:
You have created 2 scenes.
Scene_1: Captures your LOL Client
Scene_2: Captures your Browser
In the scene switcher you select the program (for example: pvp.client [or w/e it is ^^]) and select scene_1 and click the + sign. Same procedure with your browser, but now you select scene_2.
This should resolve your problem.
Edit1: switched scene_1 and scene_2