It is lawful to kill a cat if you're in danger. Doesn't matter if you have a hunting license or not, you can and should protect yourself. Not sure about protecting stock, but I would guess no one will get in trouble for doing so.
Off topic a bit, but would it be a good thing to get a healthy population of big cats here so we could have a hunting season? From where I sit and type it is as I'd like an opportunity to hunt big cats, but I bet farmers and ranchers wouldn't think so.