Stephanie Brown and Jack Drake died specifically *because* Tim was Robin. It was fascinating that Tim would run himself ragged to "undo the death" that he wasn't specifically "connected" to.
There's no mention yet of Time Travel. Maybe Tim wants to keep that to himself until he is (a) absolutely certain time travel was involved and (b) feels he can't find/rescue Bruce without Connor.
Lex Luthor doesn't consider himself a bad person. (Aside from all the murders, I guess.) This may become a matter of what Lex considers "good" vs. what Connor considers "good."