Surely VGA would have more latency than DP for an LCD? It's gotta convert from digital to analogue and then back to digital again at the other end.
Is the overhead of the protocol really greater than that? (genuine question)
But to answer your question, digital to analogue and analogue to digital conversions tend to be so fast that you don't notice. It is more of a convention thing that most VGA devices will display the image as the signal arrives, which means they have almost no latency. DP devices, on the other hand, tend to cache the image, do processing on the entire frame, and only then start the presentation.
As a result, for VGA the latency can be less than the time that it takes to send the entire picture through the wire. For DP, it always is at least one full transmission time of latency.
If the required video data rate is lower than the link symbol rate the micro packets are stuffed with dummy data to make up the difference, and up to four micro packets may be sent in parallel over separate lanes, so some buffering is required, but this need only add a few microseconds of latency, which is not perceptible. Of course it's possible for bad implementations to add more, but the protocol was designed to support low latency.
In that case, I'm guessing the latency is coming from the fact that most LCD screens are caching one full image so that they can re-scale it in case the incoming video resolution isn't identical with the display's native resolution.
I vaguely remember there being an experimental NVIDIA feature to force scaling onto the GPU in hopes of reducing lag, but not sure that ever got released.
Where CRTs do have an advantage over LCDs is response time, which is generally a few ms even on the best monitors but basically nonexistent on CRTs.
But overall, a good monitor is only about half a frame worse than a CRT in terms of latency if you account for response time. At higher refresh rates it's even less of an issue; I'm not aware aware of any CRTs that can do high refresh rates at useful resolutions.
Got my numbers by glancing at a few RTINGS.com reviews: https://www.rtings.com/monitor/reviews/best/by-usage/gaming
