I don't understand why Batman would even bother lying to Superman about having Krytonite in the first place, or why Superman would be angry about it. The only reason Batman has it is because Superman gave it to him in case of an emergency.
https://imgur.com/a/RJpebl0 He doesn't have it on him because he thinks Superman is suddenly going to become evil and is just waiting for it to happen because he doesn't trust him. He has it on him all the time in case of things like mind control and brainwashing. Which are pretty common occurrences in the DCU and Superman is well aware of this. It's meant to represent the huge amount of trust and respect between them yet it's treated as a negative thing which I just don't understand. Batman may have trust issues and be inherently skeptical of others, but he's not some paranoid nut waiting for all his friends to betray him.