I think that part of the problem is the refusal to state the obvius things in a blunt way. I mean, when they lie, one of the things we should just say is "that is a lie" or "facts doesn't support your claim". Then follow with "If you actually believe that lie you are really gullible, and if not, you are a liar and manipulator". And then walk away, because no discusion can happen until they stop believing lies. Just like that, left them in the middle of the sentence, refuse to listen. Period. And treat them as we would treat an unreasonable teenager throwing a tantrum.

That won't persuade most of them, but it would make them feel bad. Which is exactly the point. They should feel bad about telling lies.