Only when you have problems that require one.
Since you are having trouble with eggs disappearing, and you already have that style of latch, I would definitely add a lock. It's quick and easy, and will probably solve the problem. (Just don't lose the key or forget the combination, and do consider who else needs access.)
I've only had chicken coops with internal nestboxes, so I had to go inside the get the eggs. The coops have always fastened with a carabiner & latch, or an actual bar across the door. I would not hesitate to add an actual lock if something or someone got in anyway.
