It's clear from the events of Dawn of Justice that Luthor knows who Superman is, given that he eventually
Kidnaps Martha Kent as leverage,
but there are times in the movie when he also seems to know who Bruce Wayne is. For example, when Clark Kent and Wayne meet for the first time at one of Luthor's parties, Luthor acts as if the meeting is somehow historic. At the end of the movie, when Batman confronts Luthor directly, Luthor responds:
LUTHOR: This is how it all caves in. Civilization on the wane; manners out the window.
The way he puts emphasis on the words, and where he pauses, it sounds like he's saying "caves in Wayne Manor", which would be a direct reference to the Batcave. But there's no real evidence by his behavior that he knows Batman. It's possible he just doesn't care yet, but it seems like Batman got the best of the situation
by sending Luthor to Arkham
and Luthor didn't resort to threats of blackmail to avoid it.
Is the intent that Luthor knows the identity of the entire Justice League (given that he also had access to the other metahuman files at one point), or was this just overly-clever writing?