Input lag is massively affected by framerate and it's easy to prove. Go into your PCs display settings and lower your desktop's refresh rate as low as it'll go (30Hz or lower). Then move your mouse around on the desktop and you'll understand exactly what I'm talking about.

Think about if for a minute: let's say you click your mouse in between frames. That click isn't going to register until the next full frame. The lower your framerate, the more likely this will happen, leading to more input lag. This is so obvious once you spend 15 seconds to actually think about it, that I can't believe I even have to explain it to you.