"Jesse Eisenberg is Alexander Luthor Jr. of Earth-3 The impression I got from watching BvS is that Eisenberg-Lex came from a very rich family. One of the scenes in the movie takes place in Eisenberg-Lexs fathers study, a room thats not too shabby. In some ways, I got the impression that Eisenberg-Lex inherited LexCorp and was not the founder of the company. I checked the official web page for LexCorp and it is noted that Eisenberg-Lex is the CEO, but it is never explicitly indicated that he created the company. If LexCorp was inherited by Eisenberg-Lex, then that could mean that Eisenberg-Lexs father was also named Lex Luthor (or he named the company after his son, but in BvS it didn't sound like Eisenberg-Lex had the best relationship with his father). This all leads me to believe that there is a possibility that Eisenberg-Lexs father was also named Lex Luthor, and that he created LexCorp.
If true that Eisenberg-Lexs father was also named Lex Luthor, this wouldn't jive with comic book history at all. Lex Luthors father was named Lionel Luthor, and if BvS taught us anything, it's that the names of the characters' parents are important (MARTHA!"). Using comic book history as my guiding light, Lex Luthor of Earth-1 never, ever, had a son; however, Lex Luthor of Earth-3 did, Alexander Luthor Jr. Its possible that Eisenberg-Lexs father is Lex Luthor of Earth-3.
Ill admit that to come to this conclusion means that Im straying from comic book history a bit because Lex Luthor of Earth-3 died while his son was still an infant, he never created LexCorp, and he never stepped foot on Earth-1. But what if after the Crisis, the Earth-3 Luthor family got folded into Earth-1. I can hear the bat guano chants now, but bear with me for a minute.
Remember when I said that not everyone forgot that Crisis occurred? One of those individuals in the comics was Luthor Jr. of Earth-3. For my theory to work, it's going to have to be Luthor Sr. of Earth-3. Luthor Sr. creates LexCorp, a business that's about protecting humanity, because he witnessed Crisis, wanted to keep tabs on the meta-humans he knows about, and was looking for others that got pulled into Earth-1 with him.
Bat guano! Maybe, but how else does Eisenberg-Lex know about Bruce Wayne being Batman and Superman growing up as Clark Kent? It's because his dad told him. Ill admit, Im stretching a bit here, but Eisenberg-Lex was portrayed as someone who is not all there mentally. I believe that Eisenberg-Lex is a little off his rocker because he's not from Earth-1. Dealing with that realization plus the fact that meta-humans are running around messed with his psyche.
To fit my theory back into comic book history, I believe that we haven't seen Eisenberg-Lex's father because Eisenberg Lex killed his father just like Lex Luthor of Earth-1 killed his father, Lionel Luthor. If Eisenberg-Lex is Luthor Jr. of Earth-3 and he killed his father (Lex Luthor of Earth-3), it puts a spin on Crisis on Infinite Earths when Lex Luthor of Earth-1 killed Lex Luthor Jr. of Earth-3."