The images originate at the Daily Mail where it's noted Adams is in-between takes.
Well, Adams is wearing her engagement ring in the photos leading to speculation that Lois Lane is engaged in Batman Vs. Superman.
A simple check of Google images brings up pics of Adams in public wearing the same ring.
She's engaged (like for five + years) to Darren Le Gallo.
via Just Jared:
"Batman v Superman: Dawn of Justice" has a March 25, 2016 release starring Ben Affleck as Batman, Henry Cavill as Superman, Gal Gadot as Wonder Woman, Amy Adams as Lois Lane, Laurence Fishburne as Perry White, Diane Lane as Martha Kent, Jeremy Irons as Alfred, Jesse Eisenberg as Lex Luthor, Ray Fisher as Cyborg with Callan Mulvey, Holly Hunter and Tao Okamoto in new character roles for the film. Justice League is to follow directed by Zack Snyder as well.