She's lying to protect their relationship with their father--she's lying to them so they think their father is a good man, and he's not. I did the same thing in my divorce. There are so many good reasons to do this, among them that children carry part of their father in themselves, and any criticism of that person is a criticism of them; that if I interfered with their relationship with their father, they might be taken away from me; and that expecting my children to deal with my emotional trauma would be wrong and damaging for them.

And after all, in their relationship with their father, he has been a good man; they won't be in the same kind of relationship with him as I was. And I could, and did, slowly teach them how to manage and protect against the parts of him that were bad for them.

But I think the real reason Alicia is doing it is that she is in too much pain to think about it clearly. None of my reasons hold for her and her teenage children; they are old enough to understand a simple statement of fact, "Your father lied to me about how many women he'd had affairs with."