Caits only resets if she loses the target or the target has been killed. Is she gets silenced or stunned ect... she goes on CD. Though i am not sure about mana cost, i never paid attention to that part.
So about the poke. Yeah sure they target one champ and the similarities end. Lucians is an AOE straight line shot. While MF hits one other target that is manipulated by range, target type, and impure shots marks.
Ez is a channel. It has a really long cast time and is stoppable.
Then corki and kog have same ullts by your logic. They both use the ammo system. Vayne and Lucian tumble system are the same also, cause they get bonus damage out of it. Varus and Ashe are the same they have ULTS that lock down people.
You can make several champs look the same. Hell graves was called mf 2.0 when he was first released. The fact of the matter is that MF and Lucian bring different things to the game. No one will ever say that mf is a mobile champ. And no one will ever say that Lucian does AOE damage.
You keep locking on to these small things and not seeing the bigger picture. A lot of champs have 1 or 2 things similar. That does not even come close to making them the same.