Lawyer Michael Avenatti has generated a lot of media attention in representing Stormy Daniels in a lawsuit against President Donald Trump. But it’s his statements about Michael Cohen, the attorney behind payments to the adult film actress over an alleged affair with the president, and his disclosure of Cohen’s bank records that have sparked a legal ethics debate.

Avenatti told Bloomberg Law he doesn’t “believe there’s been any violation of any trial publicity rule or any other ethical rule in...