Things to ask about this question, I doubt there is an sort of official answer:
a. Can they tell when they are taking damage?
I would say yes, damage has a cause. Damage from a fireball burns; damage from a sword cuts; damage from a sap is non-lethal, it is still damage just damage that won't kill you. So, under that criteria I would say yes.
b. Can they differentiate between lethal and non-lethal?
This one is a bit trickier and I think depends on the metagame infiltration. Such as does the character know how many HP they take from falling off a cliff or from a greatsword roll? I would say the character probably has zero chance (or should have) of figuring out things like actual numbers. That said, the player certainly does track such things and so should know if damage is non-lethal or lethal. I would say yes, they can tell the difference. I would say so as the source that deals non-lethal vs. lethal is different.
c. What roll do they need?
See above. Keep in mind that most sources of non-lethal are from exhausting sources and not from weapons, but that doesn't mean they shouldn't know they are being harmed. If you push yourself when exercising you typically know you are, the side effect in-game is that you are accruing non-lethal damage. What roll do you need to tell if you are damaged by a sword? I would figure the blood trickling down your arm would suffice. What roll do you need to tell if you are damaged from the environment? I would imaging the sweat and diminished capacity to keep going would be a good indicator. For a sap? The bump on your head. I would say no (they don't need to roll) as people can innately feel damage regardless of source, it just feels different.
I mean in a certain metagame sense it makes sense to ask this question but I just don't get it entirely. I find this to be a bit of an odd question. I would similarly find 'When you take lethal damage, are you aware it's lethal? If not, is there a way to tell with a Heal check or something?' to be odd.