I think it's imperative that you understand the person who's 'covering up' doesn't see it as a lie. There's a difference between deceit and avoidance.
I invited a friend to meet and go out; when the day before came, I was paralyzed with a fear, I just did NOT want to go and meet. I can't explain it. So I 'invented' a reason why it wouldn't work after all, and backed out. Did I feel horrible? Yes. Did I feel relieved? Yes again. Do I understand why I did it? Nope. It was a 'lie', but it was also self-preservation. And all I knew was that it was what I had to do, at that time...