I personally have built stairs before and no one in there right mind is going to put a lip like that on the top of a stair...on the side yes but on the top no just no
The slabs on top of the stairs wouldn't be going up and down, if they did they would make those stairs very uncomfortable to walk on. And what would be the point?
You know, when I look at this picture, I can see both the cat going up and down, but when you think about it logically... The cat is going up because of the way the end of each stair is up a little.