The 223 is a powerful round and can kill most any animal in north America, IF placed properly and under the right conditions. Mountain lions are thin skinned, like a deer, BUT, I would not want to shoot an ML with one only to find out the bullet didn't penetrate or it hit a shoulder bone, and the cat is mad at me.
I have no doubt it will kill one, but shooting a single shot, I'd want a 243 or bigger, and that would be with something like a Sierra HPBT or heavier. Maybe hunt yote with a 243 and 90 or 95gr SP bullets.
I was reading an article about a lion hunting guide, and he used dogs. We wants them killed NOW, as he doesn't want them dropping on top of his dogs. Handguns he will allow nothing smaller than 44 Mag and 30 cal or bigger in rifle.