Yes. It isn't illegal to kill a human. But it probably is illegal for a human to kill a lion.
Definitely illegal to kill a mountain lion in Colorado. Here's some detail:
It is illegal to obtain a mountain lion license or hunt lions without a mountain lion education certificate issued by Colorado Parks and Wildlife (CPW), attesting to successful completion of CPWs Mountain Lion Education and Identification Course.
Colorado Parks and Wildlife requires hunters to allow collection of a small tooth located just behind the lions upper canine.
The tooth will be analyzed to determine the lions age. Hunters can help by making sure the jaw is propped open with a stick before rigor sets in and not having the carcass frozen during inspection. The animals age will be posted on the website 6 months after lion season ends.
Ages will be posted by seal numbers, so hunters should write the number down to check the age of their animal. For privacy reasons, hunter's names are not posted.
Thank God this one was still growing when it tangled with a strong, survival-motivated human.
Outcome of a hand-to-claw/teeth combat between a man and a full grown mountain lion is pretty much predictable.