At a news conference Friday, the lawyers said the search warrant, which allowed investigators to look for drugs, should have never been issued.
They also called for the firing of police officer Amber Guyger.
The local Fox television affiliate, KDFW, was roundly criticized for its initial reporting on the release of the report on the search's findings, drawing scorn from figures across the political spectrum for focusing on the marijuana, tweeting: "DEVELOPING: Search warrant: Marijuana found in Botham Jean's apartment after deadly shooting."
On Twitter, the ACLU called the tweet an "attack on an innocent man."
Fox News contributor Guy Benson commented on Twitter, "Irrelevant. 100% irrelevant."
National Rifle Association spokeswoman Dana Loesch tweeted: "How is this germane to what happened?"
KDFW, which later updated its story and added more context, declined to comment Friday about its initial coverage of the search affidavit.