Well, we don't know when the statue would be built, but if it's already there during the events of BvS, I think it would be more fitting for Lex to destroy it than Batman. Lex hates superman and wants to see him suffer. I wouldn't put it above him to destroy it if he could. He would think it's offensive that humanity would build a statue to honor an alien that was born with its genetic gifts. But batman is not that petty or disrespectful. If batman acts against supes, it would be for a more noble reason than hate and hate is the kind of thing that would lead someone to smash a statue in honor of someone.