I can understand you because I'm in the same boat. There is no hope to repair your relationship with you former friend not because you haven't tried but because she feels what you did was unforgivable. There are many unforgivable things in the world and you did one in her mind.
My brother's wife had a group friend(best man at that wedding) who got the microphone to make a speech at her wedding. And talked about how my brother helped feed Japanese people bananas. A reference to a show about an Okinawan performance involving a banana and a woman cutting a banana without hands, feet or mouth. It's a show you only go to once. You would have to know the story to catch the reference because it is an obscure reference that only friends knew. And both, the best man who made the speech and my others brothers wife who handed him the microphone were kicked out. He was explicitly told that he could not make speeches and instructed the DJ to not give the mic out to anyone. The relationship has mostly been repaired with my others brothers wife and her. But what was once a close relationship with the best man is now more than a will talk maybe but I really don't like you. This was a relationship long before my brother ever meet her. The best man introduced them at a college party..
my own situation is I had a circle of friends which joined up with my brothers circle of friends and we all know each other. We were all friends for over 10+ years. But what happened once I moved back home. The dynamic changed my friends were now friends with my brothers and his circle. And I got cut out of the circle and am not getting invited to the parties that they have every 6th months or so. It could have been that I was a socially awkward weird person for a good chunk since I moved back, or when I ask why I'm not invited any more they say I don't drink and it makes them feel uncomfortable when they are drinking. Or it could have been that someone believes that I am living in sin with my lifestyle and I was cut out. I still feel a little jealousy when I see the pictures of the parties.
Friendships are mutual. And your mutual friends thought it would not be appropriate to invite you since you are no longer friends with Lucy. It sucks.