You seem to completely misunderstand what the timer display lagging actually entails.
Because the display has a lag of 0.2 sec (or whatever), the time you see on it (which is not the same thing as the time being measured within the timer (*)) is going to be less than the actual time.
If, somehow, the display had no lag at all (this is easy to do; just add on the estimated lag (**)), then it would have been showing the real time, which is not sub-3 regardless.
(*) which, to be pedantic, is also not the same thing as physically elapsed time, but assuming that the timer is functioning properly, these values should be very close
(**) Exercise for the reader: what are the downsides of doing this?