Do the "stop" technique, and say EXACTLY the words I suggest above. If need be (if he persists with the "just friends" thing, or anything else you KNOW FOR A FACT is a lie), repeat it a second time.
If he STILL persists, and lies to your face a third time, GET UP AND END THE CONVERSATION, saying "When you are ready to stop lying to me, and speak to me calmly and truthfully, we can continue this conversation. I think I deserve at least that much. We're done for now."