So for example, if I encountered a troll and had never done so before, and struck it with a normal battleaxe...could I tell I was striking for non-lethal damage?
I cannot see a reason why you should, as a rule, be able to determine.
In this specific instance, I find it particularly implausible. How would a character, even a fighter used to using weapons professionally, who knows nothing about troll anatomy, the thickness of their tissue, etc. be able to tell from the split second of contact in a dangerous battle (as you imply with 'the gaps tighten slightly'), or subsequent fleeting observation whether the damage is liable to cause death if sustained or not?
The distinction between lethal and nonlethal damage is largely a game mechanic not a real-world one; almost all the examples in this answer could kill, and to split hairs slightly, the description of regeneration says that the lethal damage is converted to nonlethal damage (implied later as fire etc. doesn't convert) which is then healed. (On a careful reading I don't agree with Danikov that the damage remains lethal, "the creature automatically cures itself of nonlethal damage" implies that this damage is now definitely nonlethal, as does the use of 'convert' and the line "An attack that can cause instant death only threatens the creature with death if it is delivered by weapons that deal it lethal damage.").
By default, characters cannot even determine how wounded enemies are (although the players might know), except through means such as Deathwatch. As in real life, an assailant does not know what the effect of their attack might be until the victim collapses or similar.
If characters have a reason to think the damage they are dealing is nonlethal, if the players can describe how their characters trying to determine this then I'd perhaps allow a skill check in certain circumstances - for example a heal roll to determine if a creature is dead or unconscious (with severe penalties for unfamiliar races), or, at a higher DC, to get some description an opponent's injuries (the roll should be hidden so the players can't be entirely sure if the info is accurate). However you'd need to be careful not to eliminate the benefit of Deathwatch.