Even free speech absolutists agree that falsely yelling "Fire!" in a crowded theatre in order to cause a fatal stampede is (and should be) a criminal act. But the crime is not the utterance of the word. You could commit the same crime by setting off a fire alarm. In either case, the crime is in the action of tricking a group of people into stampeding.
Similarly, impersonating a police officer is illegal. You could do this by lying (telling a gullible person that you are a police officer), or by wearing a police uniform in public. The criminal action is tricking people into thinking you're a police officer, whether you do it with lies or clothes. Lying itself is not illegal, but a lie may constitute an action that is criminal.