They don’t tree them, ideally they catch and immobilize them, holding them in place for the hunter to kill them with a knife. As hunts can sometimes range for sixty or eighty miles through extremely thick brush, and dogos rarely bark, it’s often the case that the hunter is nowhere close enough to come help in time once the cat is caught. In that case, the dogs kill the cat themselves, but often a dog or two goes down with it.
Also, there is a training test called a Prueba de Campo, where the dog is put in a pen with a puma for a few minutes–the dog doesn’t kill the cat and isn’t left in the pen long enough to hurt it, it’s just a test of the dog’s willingness to engage and a training tool. I’ve seen videos of this, and if the cats’ claws weren’t blunted, many of the young dogs would be quickly dispatched.
So, all in all, I’d say that a trained pack of specially bred puma dogs can often kill a puma, it’s pretty likely that almost no dog would stand a chance in a one-on-one encounter with a cat that’s ready to stay and fight.
About the Lion dogs, are you referring to the Boerboel or the Ridgeback? Boerboels (if I recall correctly) are mostly used to deter baboons, leopards, and lions. They’re extremely noisy and melodramatic, and put up a HUGE show of aggression, but they don’t engage the lions at all. Lions are also MUCH larger than puma.
~mixie