you first have to pass a "mtn. lion hunting course" which you can do on line to get your license. Colo. has a quota for lions and each unit has a different quota. So you need to check daily to make sure the quota for the unit that you plan to hunt has not been filled.
The on-line course isn't that tough, but you must pass it before you can buy a license.

By the way, congrats on the cat. How did they hunt it? with dogs? call it it? Spot and stalk?