Back in the 1980's I used to meet up with a friend of a friend who carried a beagle in a pack basket and snow shoed (cross country skied) around until he cut a cougar track and then would track it out until close then put the dog down and the race was short. He shot a lot of lions, and to the best of my knowledge the beagle was never killed.
Why a lion would go up a tree instead of kill that beagle was always a mystery to me.