Law enforcement (being allowed to lie) already uses the "we've had noise complaints" or "there was a X crime in the area" bullshit to harass people they have a "hunch" are up to no good.
"Being allowed to lie" means something different. Let's say you plan to smash in a car window. A person you don't know is watching you. The prudent person that you are, you ask them "are you a cop"? The answer is "No", you smash the car window, and the cop arrests you. That's the kind of lie a cop is allowed to make. Now let's say he turned his back on you, and you smashed the window without him seeing you, but he heard you, and there was nobody else who could have done it. Later in court the judge asks him "did you see this man smashing the car window" and he says "Yes". That's the kind of lie he isn't allowed to make.