I know how your heart feels. My eldest always had a tendency to lie and hide things, for fear of getting into trouble at first. Like you, I always made them aware that lying was worse than the mistake, because it just made things worse. It used to be that she would admit it when caught out and we'd discuss things, but as she got older the reason for lying became more about an attempt to control our perceptions of her and sometimes even to try and make her sister look bad, to raise herself up in our eyes. Unfortunately, this only compounded things, because we were seeing her lies, but she would not acknowledge them any more.
She's been diagnosed with "crippling self esteem issues." It explains a lot about her behaviour, unfortunately while she still continues to try and control her environment she's pushing people away from her. I hope that she will improve, given time, but at this point I'm finding it hard to imagine regaining any trust in her, which is, ironically, what she sees as showing her we love her.
I often think back and wonder where we might have gone wrong for her to have such a low self esteem that she constantly feels the need to prove herself. She feels like we favourite her sister, yet for the most part she got the most attention, because she demanded it and her sister just got dragged around after. Perhaps this was the problem, because when I realised what was happening and tried to balance things out better, she might have struggled with not being the centre of attention.