Supposedly, Eisenberg's Luthor will be into tattoos big time, and have a sleeve of the Metropolis skyline down his right arm. He also became a self-made billionaire at 18, and is the CEO of Lexcorp.
Despite currently being a ruthless businessman and complete tech genius, he's also got street smarts. At the age of 14 Lex was on the streets and it wasn't long before he was initiated into a street gang. Within a year, he was their boss. His resolve is his main weapon, and alongside being incredibly intelligent he's also got where he is thanks to his own hard work.
Which is why he isn't a huge fan of Bruce Wayne, who he believes had his success handed to him. This explains why the first meeting between the pair early in the film is so tense, when Wayne pays Luthor a visit in his Lexcorp Tower penthouse. Bruce is impressed by Superman, Lex views him as an alien invader who shoudn't be here.
Wayne wants to pool their resources to philanthropically rebuild Metropolis and, while Lex is sceptical, he reckons he can use Wayne Enterprises and Bruce for his own ends. While Mr. Wayne believes there to be a peaceable resolution available with Superman, Luthor reckons there's a different solution, and one that can be achieved without him having to go anywhere near the front line himself. Which is where Batman comes in.