The reason a CRT seems to flicker with low refresh rates is because the screen goes dark in between beam traces, a LCD does not. So a static image on a LCD with 60 Hz refresh rate is stable whereas a CRT would flicker at that rate.
It's much more than that; the flickery 60Hz CRT is only incidental, it doesn't relate to the perception of smoothness. Like a sibling comment to yours says, it's very noticeable with the mouse, and even more so when moving around a window on the desktop. It looks like crappy stop-motion animation compared to what it can be at higher frame rates.
Just how old are your lights? Fluorescent lights haven't flickered at line frequency in at least a decade.
Well, obviously old fixtures still exist, but if you have one in your office it's time to get rid of it. The new ones are much more energy efficient, but more importantly they are more pleasing to the eye.
