It has nothing directly to do, with input (directly). One frame interval allows your CPU to calculate the next frame, while your GPU draws the previous. When it is off, your CPU has to wait till the GPU has finished drawing, before it is allowed to calculate evereything for the next frame frame.
To illustrate
OFI off.
CPU draws for 8 ms (Frame 1) after that GPU draws for 12 ms (Frame 1) after that CPU draws for 8 ms (Frame 2) after that GPU draws for 12 ms (Frame 2) and so on. resulting in 20ms per frame.
OFI on.
CPU draws for 8ms (Frame 1) after that GPU draws for 12 ms (Frame 1) while CPU draws for 8 ms (Frame 2). GPU draws for 12 ms (Frame 2) while CPU draws for 8 ms (Frame 3). resulting in 12 MS per frame after the intial frame.
Because your CPU is the one working out input. It has already done all calculations a bit sooner than before, which means that the frames are calculated with older input data. However keep in mind.
OFI only calculates 1 frame ahead at most. There is no runaway effect.
The inputlag it generates is frame dependend i.e. fewer FPS higher input lag since OFI increases FPS it partially offsets the negative by providing overall faster updates of your gameworld.
My personal view is to keep OFI on at all times. You could propably have it off, when you reach your desired target FPS without it. But at 144 fps, I would argue the inputlag it might generate is very low anyways.