My immediate concern is that your lion will likely get bored. An underground pen where nothing happens except food falls in a few times a week. If he gets too bored he will jump out when the trap door opens and look for some excitement.
You could make the pit deep enough that he can't jump out, and then probably the food will die when it hits the floor and the lion is not much use.
It sounds like you have the lion trained to stay in the little pen behind a thick metal door so it can't get out while the trapdoor is open. I'm sure this is even more boring, but you could tell the lion trainer to just send it behind the door when you're about to dump somebody in the pit, so they don't land on the lion and hurt it, and the lion can't jump out.
I think the better solution is to have a pleasant outdoor environment for your trained lions, and only send one in when you have a job for them. Of course, this provides some chance that someone can get past the lion and outside, into the lions' den.
Don't depend on humans to feed your lion. That's likely to leave you occasionally killing people who haven't done anything wrong, just because the lion is hungry. And that will make your minions less loyal.
Also if you don't feed your lion regularly to make it extra hungry when it finds a human (who is likely to smell bad, and be covered with inedible uniform, and who might even be armed), the lion is also likely to be less loyal to you. He will want to get away.
Better to get the lion trainer to teach the lion to play with a human-size dummy. Like a cat playing with a mouse. Maybe sometimes give it humans to play with for part of the training. If you teach it to play with humans on command, for a reward, it is less likely to do it on its own when it won't get the reward. That's an extra benefit.
So when you dump the human in and the cat gets the signal to play with it like a mouse, you get lots of fun and the cat gets lots of fun, even when it is well-fed. Just make sure the human can't hurt kitty. If he manages to kick the lion in the jaw and damage its ability to bite, that will be a very sad kitty long after the man is dead.
I don't know much about lion training, and I wonder whether they would like catnip rewards. I'm sure food rewards are good.