Police can lie in an interview. They can mislead, too. In fact, they often mislead a suspect into believing they know more than they do. It’s good police work.
They can’t lie in the courtroom though. At least, not with immunity.
The only person allowed to lie in the courtroom is the DA (prosecutor). In fact, he’s expected to lie. By lie, I mean promote facts that he merely assumed may have happened, regardless of whether he has any rational reason to believe they actually happened. The DA is free to be as creative as he chooses with respect to interpreting the evidence.