It is a fact that they didn't show him finding out in the movie, but this is not a plot hole. It is implied that Lex knew the identities right from the beginning of the movie, and the filmmakers have recently confirmed as much. We never see how Lex figured out Superman and Batman's secret identities. Also, remember scenes that are edited in close proximity do not necessarily happen in that same timeframe. If, however, you insist that this is too coincidental, then I would say that Lex could have easily had a team in-the-ready to kidnap Martha and also some sort of intell on Batman's movements (he knows his identity, after all) and when he saw that the fight was going down, he ordered the kidnapping. But unlikely things happen all the time in movies and they don't fit my definition of plot hole, which is a logical inconsistency or physically impossible event (within the laws of the movie). It is just two events that (may have) happened in close chronological proximity to one another and some people thought it was unlikely for them to happen like that. Lex had no way to perfectly time Martha's kidnapping with the moment Batman turned on the bat-signal. Ultimately, Lex ends up getting the entire corpse to use for his own purposes in the scout ship. What Lex was negotiating for was more access or a greater extent of access to the corpse. A plausible explanation is that Lex's scientists had temporary access to Zod's body but that the body was still in the government's possession.

Wait, didn't he already have access to the body? This is not a contradiction. Lex ran tests on Zod's body but then tried to secure possession of Zod's body. Here is an audio version of the text below. (So a fair criticism would be that BvS was difficult to follow, but an unfair criticism would be to say that it didn't make sense.) Although I do not doubt that the Looper author was confused by these things, I do not think they hold up as real plot holes. I'm going to run through the 9 purported plot holes from Looper.

Batman v superman bat signal gif