Sam, I actually think that you handled the conversation extremely well. You made your points, you did so without accusation or anything more than an authentic amount of righteous anger, and -- as others have noted -- with that all being said, now you should DROP IT.
If he flat out lies to your face, you should certainly put your hand up and say "Please stop it -- we both know you're lying to me right now," and make that a personal boundary, but there's no reason now to keep having this same conversation with him now that you've spoken your peace.
