The reason for this issue is that Mortal Kombat (at least II, probably others, as well) does in fact run at a strage, low refresh rate. While most games run at about 60Hz, MK runs at ~53-54Hz. This may be due to the fact that arcade games of that era generally ran the "event loop" once per frame, and so if the event loop needed to do too many calculations, the hardware may not have been able to manage normal 60Hz refresh as the event loop wouldn't have finished by the time the next frame rolled around. It may also have been that they wanted higher resolution graphics, as there's a trade-off between resolution and refresh rate if you want compatibility with a standard monitor.
That said, most LCDs do have a smallish range that they'll accept. For PC LCDs, it's usually "a little below 60" to "a little above 75". This is done since many PCs output their BIOS startup screen at 72Hz. It is also handy for watching movies (72Hz = 3x 24fps which is standard movie rate), though this feature seems rarely used. Many cheap LCDs probably downconvert anything that isn't "about 60". TV LCDs are usually much more limited. US ones almost universally accept nothing but "about 60" and perhaps "about 24". European ones are usually a bit more forgiving as they try to be compatible with both European PAL TV timings (50Hz refresh) and US NTSC timings (about 60Hz).
My (admittedly high end and also quite old) PC LCD will accept anything between about 47 and the low side of 76Hz, and it seems to display it natively. I certainly can't get it to tear even on deliberately rigged test signals, but I don't have a super high fps camera needed to actually capture all the timecodes to see if it's not doing frame dropping. The motion seems smooth, at least.
Unfortunately, the ~53-54Hz used by MK and friends is probably outside the range of what many cheap PC LCDs will accept, but you can at least try it. The challenge is often getting Windows to actually output what you want: most drivers on Windows will limit you to things it THINKS your monitor can do and will often go so far as to silently give you something other than what you're asking for.
Anyway, to resolve the issue you're having, assuming your monitor can handle the native vidoe, most people seem to use a MAME frontend that supports switching up some system settings prior to launching MAME itself. The frontend can tweak things like refresh rate prior to starting a particular game. MAME also has its own ability to switch graphics modes, but I'm not very familiar with it, and people seem to constantly whine about it not working right or being difficult to use.
That said, there's little reason to output native video to an LCD, though matching the frame rate, if possible, can be useful. Honestly, if I'm using an LCD for this, I'd just always output native resolution at a fixed refresh rate and tell my emulator to scale and frame dupe/drop to "make it work" (triple buffer would do this). The vastly different response profile (and, often, input lag) on LCDs and upscaling required to make it take up the whole screen (though PLEASE maintain aspect ratio) already destroy any "native display" effect I may be seeking. It's just a matter of making it work, at that point.