Oh, you poor thing this sounds really hard, I hope you are okay. It sounds as though you felt like you were in a genuine relationship with this person albeit with Lucy being a constant troublemaker. Ultimately it hasn't worked out and your relationship now feels like it was never real and that you must an idiot for feeling that it was. That is so hard because it makes you question your own judgement.
There are a few possibilities, but first I think you have to accept that Lucy was never a friend, and she certainly doesn't seem to have had your best interests at heart. Try and stop trying to work out why she has behaved so badly, it's because she isn't a nice person and was never really your friend, just someone you shared space with for a while. That's all that matters really.
With the relationship, I suppose it is one of two possibilities, either it never was real and you were being played. That might be true, this person might be skilled at stringing people along for their own amusement and seeming more engaged than they really are. If that is the case you have nothing to feel ashamed of, you have been the victim of a player and although that will make you feel horrible they aren't worth your time. People like this often end up sad and alone as they fail to make any real long-term connections.
Alternatively, it was real for a time for both of you, but it has run its course and this person doesn't want to continue. That might be because of Lucy or it might just be that this wasn't "the one" for both of you. In a way, this is easier to accept because it means you weren't cynically taken for a ride by someone you had feelings for. It is sad, but relationships end and often we don't get the closure of understanding exactly why the other person has withdrawn.
Please try and move on rather than focusing on the why. You have been through some horrible stuff with social services, but you have come through it and been found not to be at fault. Thinking about the details of who knew what and when isn't going to change things and it can only prolong the time you spend feeling awful about it. That only delays you moving on to whatever comes next, which can only be better times.
I would cut ties with these people and try and concentrate on other friendships with people that make you feel happy. Life's too short to spend on other people's toxic dramas
All the best