Even tough LCDs sample and hold (so, no refresh flicker like a CRT) many employ a PWM to modulate the backlight brightness which will cause it to flicker in excess of your refresh rate, with the pattern varying according to the set brightness.
Some PWM flicker might reach a frequency that is low enough to bother you, I've read about people who bought a brand new LCD TV and had to return it due to headaches, supposedly attributed to the rate of flicking by the PWM.
Some monitors are sometimes even reviewed as not employing a PWM thus being easier on the eyes.
You will never visually see flicker on an LCD unless it's malfunctioning or you have activated black frame insertion. But the flicker is still there on PWM equiped ones, only visible with special equipment or slow motion cameras.
The problem them is that your brain might be subconsciously sensitive to some specific flicker patterns, resulting in the aforementioned headaches.
Yes, but some implementations or edge cases (like putting some TVs/monitors in it's max brightness/dynamic mode) can have the PWM frequency drop to as low as 120hz with god knows what duty cycle.
Some PWM flicker might reach a frequency that is low enough to bother you, I've read about people who bought a brand new LCD TV and had to return it due to headaches, supposedly attributed to the rate of flicking by the PWM.
Some monitors are sometimes even reviewed as not employing a PWM thus being easier on the eyes.