Fo do that sir, Launch OBS Studio on your computer, hit the Plus sign under Sources, and click Display Capture. Step 2: Select the display with the game you wish to capture and check if OBS recognizes it. Step 3: Click Start Recording to capture your gameplay.
If steaming lags, then it has to do with your system - probably it's not strong enough or you stream a high quality your system can't carry or you overload it while streaming etc...