About the possibility of Batman having a lead-lined suit: Maybe if Bats IS packing kryptonite, he's wearing a lead-lined suit to protect him from the radiation (kryptonite radiation IS harmful to humans, it just takes longer). Protecting Bruce's identity would just be a side benefit that he didn't know about. He'd probably figure it out during the fight, so he could make sure he lined his cowl from that point on. Just spitballing.
Wouldn't this armor be getting pretty heavy by this point? What the hell powers this thing? It's not an Iron Man suit with an arc reactor. Superman could just knock Batman over and he'd be trapped like a turtle upside down on its shell. I suppose that wouldn't make The Fight very interesting. Funny, but not interesting.
