The VG236H consistently lags 1 frame from the FP241W, regardless of FPS, across about 40 photos I captured of the two displays. It’s always exactly one frame behind.
So what does that mean? Well, we’re likely seeing the difference between the 60Hz refresh rate of the FP241W and the 120Hz refresh rate of the VG236H. The higher refresh rate lets the ASUS show more frames than the FP241W, giving us more granularity. It just so happens that it’s pulling one frame behind, which on average worked out to a lag of 1.9 ms.
Further, Jarred tested the FP241VW which is essentially the exact same monitor as the FP241W but in a different enclosure, and measured input processing lag to be 2 ms compared to the famous HP LP3065 (which has no scaler and no input lag). Thus, a more accurate number for input lag on the ASUS VG236H is the sum of the two, at a much more respectable 3.9ms.