Although we don't natively support game capture with fullscreen games, we do have a workaround to force games without a borderless windowed into a borderless windowed mode.
First, you'll want to download and install BorderlessWindowed from here. Once you've installed the program, run the program and double-click on the system tray icon in order to bring up the program. Next, you'll want to change the mode to "Hotkey" and assign a hotkey. Once you're all set up, simply open up the game you'd like to run in borderless windowed and hit the hotkey once to set it to windowed or twice to set it to borderless windowed. You can now open up Lightstream and capture your game using Window capture.