They have Mountain Lion hunting here in Colorado. I've never done it, but I think it would be fun and very challenging.
I don't think there is much of any risk of you becoming kitty food from just hunting them. Mountain Lions are fairly common sightings on my property - I often see them (and hear them) hunting near my house at night. When I walk my dogs those nights I carry a 12 gauge Remington 870 shotgun, but I've never had an issue.
(As background info, 'baby' mountain lions stay with their mothers for the first two years while she teaches them how to hunt. As you can imagine, 2 year old male mountain lions can be much larger than their mother. When they are on my property they surround my house and communicate with each other by 'screaching' their locations. They sound like a f&cking bird of prey. Those nights when I'm walking my dogs I shine my tactical light from my 870 around and locate the reflection of their eyeballs just to keep an eye on their locations. One night last year they took down a fucking elk across in the forest across from my house)