At the end of the Batman V Superman movie, Batman threatened Lex Luthor to brand him with the Bat symbol.
But, he didn't do it.
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Here's the scene itself
Luthor was the reason branded people were being attacked in prison. It's unlikely Luthor would be attacked for having a brand.
In the Ultimate Edition we see that Lex and company pay one of the inmates to “shiv” the latest bat-brandee in the prison yard. This is all part of Lex’s plan to stoke the fires of Superman’s outrage at Batman’s methods.
Batman runs on fear. Luthor's only card left to play (in a Joker-esque way) was to basically rub his triumph in Batman's face. In other words, he refused to bow in fear to the Bat, thus depriving Batman of any satisfaction in the visit.