Lots of LCDs have exponentially more input lag when you drop them from their higher refresh rates to lower. For instance (from data sources like TFT Central or Rtings) it's common to see a 120Hz monitor have 2ms input lag but then at 60Hz it will have 30ms.
Saying 120Hz feels sluggish is also confounded since the mouse / keyboard have 8ms lag unless you use a gaming one or manually change the polling rate, and games and desktop implementations all have variable input lag up to 100ms or some crazy number. Whether your desktop has vsync is another variable.
None of this of course changes the fact that input lag on a monitor should be zero aside from the pixel transition period.
I have reached the point where even the desktop feels sluggish at anything under 120hz.