Lying, whether by omission or by saying things that aren't true, is just trying to control someone else's reality. One reason we lie is to get something we would not be able to get by honest means. Another is to avoid a consequence for something we have already done. By lying we are trying to change an outcome to favor ourselves or to avoid something unpleasant or painful.
I think the reason you lie is because you want to control your BS's reality and therefore what she thinks about you and your chances for reconciliation. But a far more important question is: why is lying your go to mechanism when confronted with a difficult situation? Why is it easier and more comfortable to lie than tell the truth?
Finding the answer to that question will take a lot of self reflection, probably with the help of a therapist who knows how to ask the right questions. But. There is something you can do to aid the process starting today, right this moment. You can stop lying. It is a simple idea but it is difficult to do because you have to override what is, at this point, a mechanism that is wired into your brain circuitry.
For most of my life I have been what I would call a "spinner". Someone who would spin the truth so that people would perceive me in the best possible light. White lies, people would call them. I was late because of traffic (I didn't budget my time properly). I got this flavor because I know you like it (because it's what I wanted). They seemed harmless to me and telling these little lies felt completely natural. But they weren't harmless to me. Lying is a brain mechanism. It changed my brain. You've seen in your own life the horrible damage the lying mechanism leads to. I did too. I knew I had to stop lying to save not only my relationship with my BS but also to save myself from going through a life of further self destruction. To stop lying, I had to change my brain.
The automatic lying mechanism got built up one lie at a time. Changing it is done at the same level. One truth at a time. That means every time I realized I had lied, I had to correct it. Not just acknowledge to myself that I was lying or had lied but actually tell the person I lied to and correct it to them. Sometimes it felt ridiculous, admitting to the tiny lie I had just told. Like traffic and being late. Over time, though, I began to catch them before they came out of my mouth. It felt like just going over a speed bump. After about two and a half years of practice, I have finally gotten to the point that telling the truth is usually my first response. The old "lie first" mechanism still activates sometimes but I'm aware of it, I notice it and I usually autocorrect before it even gets out.
A bonus to this all this truth telling is that eventually I really began to be able to recognize my own lies, even ones I was telling myself in the past, including the lies I told myself to make me think it was okay to betray my husband and my own values. That's where the therapist can be helpful. But the truth telling, the brain rewiring, only you can make that happen. I'm not saying it'll be comfortable. But really, what do you have to lose at this point?