Um, I think you've got your terms confused. SVGA refers to a specific set of timings from VESA, specifiying the 800x600 PC graphics mode. It doesn't specify a display type.
There are LCDs that don't lag. Most designed for PC work don't lag at all, though some cheap ones exhibit poor response time. Don't trust the number the manufacturer specs as it's often tested in a way that makes no sense (WB, BW, WBW, or BWB is a useful measure while WG, GB, BG, GW, or GG is not). Most higher end ones are very, very good. I used to play beatmaniaIIDX on an LCD, and if there's any game that is latency sensitive, that's it. There seemed to be about 1 frame of latency on the s-video and composiet input, and zero on the PC inputs. This is probably due to the deinterlacer. LCD monitors designed for use as TVs do often exhibit latency from input to display, which is very bad for gaming.
CRT PC monitors exhibit no lag and don't have response time issues. CRT arcade monitors are similar. CRT TVs can and often do exhibit horrible latency from input to display. This is mostly a problem with cheap HD CRT sets which, rather than scan at the input display timings, scale everything to (usually) 1080i. The scaler usually has quite a bit of latency. Avoid these sets. Plain analog SDTVs don't exhibit this behavior, but don't look all that good without taking special measures to ensure things don't get scaled in the process of making things suitable for their inputs.
Note that with an LCD, all inputs must be scaled to native res by the LCD. This is a limitation of the technology, not a particular set. This means that standard res arcade games will not and cannot look authentic. With a CRT having proper dot pitch, you can get authentic looking display from standard and medium res, but display at 800x600 and above will suffer some blurriness. If you go for visual quality at these higher resolutions, standard res tends to start to flicker and the scanline artifacts become objectionable.
Your choice will largely be affected by intended use and how much you're willing to spend. The best option for most uses is a multi-sync arcade monitor, but these are expensive.
If you'd like to test latency of a monitor, you can do so with a little extra equipment. Find a laptop with an s-video output and an old analog CRT television (which will have no lag). Run a program which displays timecodes (a number incrementing every frame) on the laptop screen. Take a picture with a digital camera where both the laptop display and the TV are in the shot. This establishes a baseline latency in case there's lag between your laptop screen and the s-video output (often there is not). Also plug in an old CRT PC monitor to the VGA output and repeat, if you plan to test using that signal. Now, do the same thing with the monitors you are looking at buying. You can tell what the latency is in frames between input and display by comparing the timecodes shown on the laptop monitor and the display under test. Make sure your refresh rate is set to 60Hz for this (50Hz in Europe) so that there won't be any oddball framerate conversions going on as most TVs can only handle 59.94-60Hz (this also applies to LCD PC displays, just set to their native refresh - this does not apply to most CRT PC displays).
Example of this procedure