When you have 60 Hz monitor and you don't limit the FPS to 60, but instead let it to be higher than monitor supports (e.g 120, 140, 200 FPS), then what you'd get is screen tearing and/or frame skipping. The bigger the difference - the worse result there is. That can result in a choppy gameplay and motion blur, most visible in fast-paced games.
Input lag is completely another ballpark and has little to do on how many FPS your GPU is outputting. Input lag starts from the key press of mouse/KB and ends at the monitor screen. There's a lot of hardware between the two and they all contribute to input lag.