Her where I live, funeral processions are led by the police with their flashers and lights on. In fact, I just saw a policeman stop and monitor a traffic light to allow the procession to pass this morning.
They do that here also if using streets or feeder roads. But they often shut down all southbound lanes to let one pass, rather than just allowing them to occupy one lane while through traffic continues on the other two lanes. Guess it matters how important the deceased person was while living in the City.