They typically lay around because they are depressed or tired.

That's quite an uneducated viewpoint. Most animals (including us) move a very small part of the day. Finding food, finding mates, etc. Lions will sleep or rest for 21 hours a day. Their active hours tend to be dawn and dusk.

Beyond that, Nobody is physically poking any animals, that's not how zoos work. As someone who worked at a zoo bad behaviour is rare, it happens, but it's dealt with.