As for Lex Luthor, it would appear that he is repsonsible for the destruction outside of the new Wayne Tower (aka Corktown)
http://www.clickondetroit.com/news/batmansuperman-movie-takes-over-detroit/27342670
As seen in the image above, this is the set of Corktown. It is in this area wherewhich we have seen Bruce Wayne rescue a little girl from falling rubble outside of the Wayne Tower. What would Lex Luthory hope to achieve by staging an attack outside of the Wayne Tower? Maybe this is Lex's way of trying to convince Bruce to join him and take opposition against Superman? Tell us what you think in the comments below.
In Warner Bros.' superhero followup to Man of Steel, Henry Cavill returns as Clark Kent aka Kal-El and must deal with the fallout from the World Engine attack from General Zod's Kryptonian army. Enter Ben Affleck’s “tired, weary and seasoned” Bruce Wayne. Scheming behind the scenes is Jessie Eisenberg's Lex Luthor, who's machinations could spell doom for Metropolis and Gotham's caped guardians. Wild cards at work include Diana of Themyscira aka Wonder Woman, played by Gal Gadot. And Victor Stone aka Cyborg, played by Ray Fisher. Zack Snyder directs from a script penned by Chris Terrio. Story by David S. Goyer. "Batman v Superman: Dawn of Justice" is set to be released in theaters March 25, 2016.