I tend to agree with the posts above. I would unfriend him on FB and any other social media and keep contact to zero or very minimal. I was told by my addiction therapist that the lying doesn't stop when they get sober, that comes with time working a strong program (AA or the like) which is based on being completely honest with yourself and others. The lying is almost habitual at that point. He is asking for space and time, use that to your advantage.
My ex did the same and he did what I couldn't do for myself, which was leave the relationship. With time I realized it was the best thing that could have happened. That caused me to dive into my own recovery which has changed my life.
I also made a pact with myself - to no longer intentionally inflict pain and hurt on myself. That meant not looking at his social media, where I would invariably get my feelings hurt. Not reaching out to him because I knew I would feel more rejection. Not expecting the love from him I had been fighting for all the years he was using because he was incapable of giving that. Not asking questions I knew the answer would hurt me. He had inflicted enough pain and damage in my life, I didn't need to continue doing it to myself. Everytime I was tempted to contact him I thought about that and instead I would journal or go to the gym or clean the kitchen, go to an Al-Anon meeting whatever to get past the need to reach out.
Really give therapy (with someone who specializes in addiction) and Al-Anon a chance. Both of those are the foundation of my recovery. I was a mess and couldn't afford therapy everyday (I felt like I needed it every single day) so I went to Al-Anon almost every day for months and it was a life saver for me.
Best thing to do is just keep working on you, building yourself up, learning about the disease, and move forward. This is a gift even if it doesn't feel like it right now.