IPS displays are available that don't exhibit much if any "lag". They do have some of the slowest response time of major LCD technologies, but H-IPS is comparable to a slow TN or PVA. Of course, H-IPS is one of the most expensive LCD technologies available.
PVA displays usually do have lag as they benefit greatly from non-causal overdrive waveform calculations, so delay is required to restore physical causality. They tend to have faster response time than IPS, though, which somewhat offsets this in some applications.
TN are usually somewhere in the middle (and are commonly tweaked for low response time at the expense of input lag) but will exhibit the worst viewing angles.
It's too bad they don't make CRTs anymore...