Still lying.

I don't believe that you didn't contact her to talk about getting back together. You admitted it, and then way late in the game you said something else. It was also in a defensive situation. I don't believe you. 
Martin is right, you shouldn't be in a relationship for a while until you can do it. You can write everyday and write the truth. We can sit down and talk and practice. You an practice to yourself what that might sound like. 
You lied to me when I asked if you were actually serious about marrying me and the rings. How can it be so deeply ingrained?
You said "everyone does it" and that you are confused. The problem is that you aren't confused, you're defiant, resistant, protecting yourself from being labeled as having a problem. But you have to, because it is a problem, stop deflecting to me no matter what my part, stop saying, but... just own it so it can be fixed. You have to get over the idea that you can't stand me being somehow better than you or knowing more. I hate feeling like a child as much as you do, but humility here will go a long way. 
When you said you don't even know you do it, it's compulsive. There is that term for it, compulsive lying, please recognize this for what it is! For people who do it, they know they did it, they don't forget, they know the difference, that is why it's different for you. 
Or you're lying about whether or not you're doing it.