Absolutely, if I spotted one of these my lawn I would shoot the damn thing to Mars.
Why they are not bothering you. Cats like to attack when they have the element of surprise. Mtn lions who lay down or curl up are not threatening in any way. Now if you were jogging or hiking high up in the mountains and they are perched up on a rock and you don’t see them its a different story. I bet you could have scared kitty off with a broom. Cats know when they have the advantage.
Why would you shoot the cat? He wasn’t threatening anyone. Peoples ignorace baffles me. This kind of attitude is what leads to mass extinction of big cats and other animals in africa and elsewhere. You leave them alone they leave you alone. Besides they help control the deer populations.
So can a dog. So can your neighbor. etc