I don't know if I would say that the lion was stalking the hunter or just curious about what that strange animal was.
Many years ago we were deer hunting in Utah. I wasn't old enough for a tag but I was packing a rifle for my sister when my brother in law saw a couple of nicer bucks on the far hillside. They were in the oak brush so we just sat down hoping that they would come out into a area where we could get a shot. A short while later here came a hunter on that hillside walking through the thickest part of those oaks. He went up and over the hill and we herd a couple of shots. Evidently those bucks had moved over the hill without us seeing them. Very shortly later here came a mountain lion following right in that hunters foot steps through the thickest part of those oaks.
Was he stalking that hunter or was he just trying to figure out what was going on or what that strange smell was. Quite often I have hiked out on a ridge and when I came back I will have lion tracks right along side of mine. It gives you a strange feeling.