This guide will show you the fastest way to get the King of the Jungle achievement.
One important note is that you must have atleast a few open spots in your Ludus to house the lion (to be safe I had 5 spaces open), if not it will eat one of your men and run away. You can do this in either mode. The quickest and easiest way to obtaining a lion to fight in the arena, is by waiting until a red event box pops up into the middle of the screen that gives you a series of choices. You are looking for a particular event, one that says "Your guards have found a caged lion." If this event does not come up, hit escape and quit to menu. Then reload your game and you will be taken right back before a new event. Keep doing this until you find the caged lion event and select the answer choice "Train the lion in the gladitorial arts. It will make an impressive show in the arena." Once you do this you will have a new pet lion and also the King of the Jungle achievement.