I think you need to move on. This isn't a little white lie. This is a MAJOR lie. Yes, people make mistakes, but you waved a huge red flag in her face. You carried on a lie for months! You have shown her that you are quite untrustworthy. I think you should leave her alone and work on your own issues. You just keep on bouncing from relationship to relationship and the lying issue is still there. Take time to yourself, by yourself, to fix this lying issue. Figure out the reason for your lying. If you don't figure out why you do it, you'll just fall into old patterns again. Its a lot more than simply being regretful over past lies.