Hi! I'll be glad to be of help with this issue.
I can imagine how distressing this situation must be for you. You realize you did wrong and you want to get back on the trusting track with her. That's good. I can't say whether it's hopeless or not; you'll have to see how she reacts. But you can make a good faith effort, okay?
The best approach is to write a longish email or letter. You want to do two things in the letter: apologize in detail and make the point that you're not asking for things to be the way they were before but to try to slowly rebuild the friendship. Here's what I mean:
You want to apologize, but not just for telling her lies. You want to go into detail. What you did wrong, how you see what you did wrong. In detail about what you did. You want Michele to believe you that you actually do realize you made mistakes.
Then you want to let her know that you're not trying to pretend like it wasn't a big deal. You know it was a big deal. And so you want only to slowly rebuild the friendship. Not to have her pretend nothing happened, but to slowly let you show you're a changed person and you're committed to being a good friend.
Okay, I wish you the very best!
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