In the recent movie Batman V Superman, the antagonist Lex Luthor
kidnaps the mother of Clark Kent, a.k.a. Superman, so he can threaten him and make Superman fight Batman.
He mocks Superman by calling him "Clark Joseph Kent". I read somewhere, that Lex Luthor already knew Clark Kent’s identity at the party, where he was "so" excited that Clark Kent and Bruce Wayne met.
How and/or when does Lex Luthor find out Superman’s identity? From my point of view, it is not really obvious in the movie.
How and/or when does Lex Luthor find out Superman’s identity? From my point of view, it is not really obvious in the movie.
When: After the Black Zero Event (the attack in Metropolis) and before the discovery of a large chunk of Kryptonite in the Indian Ocean.
How: After the Black Zero Event, Lex has an existential crisis (tech billionaires are far from immune from these, Elon Musk has them towards everything from virtual reality, to artificial intelligence, to extraterrestrial life; mitigated only by the fact that none of these exist on a level to crack him yet). In his comparative and relative powerlessness (neither he nor Bruce are powerless, but they feel relatively powerless compared to an alien capable of state-level interventions and destruction), Lex clings to the only power he can accumulate: knowledge.
Lex says this explicitly during the fundraiser speech.
The files recovered by Bruce and Diana aren't just plugs for the Justice League but key insight into Lex's motives and knowledge. He combed through illegally acquired data with facial recognition algorithms allowing him to catch Wonder Woman in present day. That same mountain of data and software would fairly easily see through Superman's disguise or Batman's background. By the time the story starts in earnest, Lex has already uncovered everything about everyone.
The fact that there is no file on Batman or Superman (yet a file on Kryptonite!) in the files stolen is a huge hint.
In fact, Lex offers Bruce access to his R&D, essentially opening an alternative legitimate avenue to the same materials Bruce stole. Lex WANTS Bruce to have those files.
In some sense, this is the "what if" from the 1980s Man of Steel run where Lex decides to actually LISTEN to what his computer revealed about Superman's secret identity, rather than ignore it as impossible due to his own hubris and projections of who Superman would be, layered with an existential crisis.
Whether Lex knew about Superman's identity during the party is up for debate...
But kidnapping Martha clearly indicates that he knows that Clark Kent is Superman.
In Man Of Steel, Zod kidnaps Lois and extracts the identity of Superman and therefore goes to his house in Smallville. Now when Lex assumes control of Zod's ship,he is asked by the AI if he wants to know all the information the ship has. So,there he learns about the identity of Superman...
Lex knows because every time Lois is in danger she gets rescued (like the time in the desert when superman swoops in after Lois witnessed the death of the CIA agent). The bad guy was hired by Lex to secure the Kryptonite and kill Martha, but mostly to make sure that superman had a special bond with Lois).
This was also confirmed when Clark received anonymous photos of batmans justice). Also Bruce Wayne receives those letters blaming him of his employees death. Lex knew who Clark and Bruce are at the party. If he had info on the flash, aqua man, and wonder woman, it's entirely reasonable he would know of Bruce and Clark somehow.
Lois Lane, as an investigate reporter, was able to discover Superman was Clark Kent in Man of Steel. Presumably, Lex Luthor could do the same. He has the money to hire as many people as necessary to comb through everything known about Superman. Sooner or later, they, like Lois, before them will stumble on the connection between Kent and Superman.
Also, as mentioned in other answers, Luthor was compiling extensive information and histories of metahumans, so Superman would be most definitely included. Lex didn't neglect the Batman either, he was keeping tabs on them all.
Luthor's introducing Wayne and Kent to each other indicates he knew who they both were, presumably discovering their identities was done well in advance of what he see him doing in Batman v Superman: Dawn of Justice.
In the DCEU Superman and Batman's identities are known by more than their close confidants. It's pretty obvious at least some people in the government know who they are: Waller knows exactly who Bruce Wayne is in Suicide Squad. The military recovered Kal-El's spacecraft from the Kent farm to use against Zod and his followers, and it wouldn't take a genius to connect him to Clark.
Given that, it's trivial to assume that someone with Luthor's resources could simply bribe someone if he had to to get the information if he couldn't find it himself.
Lex Luthor was digging up information on metahumans. Clearly he knew who Flash, Aquaman, Cyborg and Wonder Woman were so I don't think we should be surprised that he also came to find out who Superman was. The guy was obsessed with Superman.
