At least at some point in Batman V Superman: Dawn of Justice, Jesse Eiseberg's Lex Luthor will have hair, according to a pair of alleged eyewitness reports from the set.
Here's what Batman News heard:
LexCorp scenes were filmed over the past two days and a source tells Batman News that Eisenberg has “a lot of hair”. It’s not Eisenberg’s typical curly look — it’s a bit longer, kind of loose and wavy, and it’s dirty blonde. Eisenberg’s Luthor has spastic mannerisms, like a 20-something guy that pounds energy drinks all day. I’m told that the scenes shot take place towards the beginning of the movie… so maybe there’s still a chance that Lex Luthor could show up bald by the end? We’ll have to wait and see.
...and a fan posted to an IMDb message board that Lex drained a basket at the basketball hoop in the lobby, shook hands with a US Senator (possibly played by Holly Hunter) and that the character is somewhat reminiscent of Nirvana frontman Kurt Cobain.