I don't think either one of them is lying. I think Andrew tried to tell her she was going without really coming out and saying it. He probably thought that he made it clear and Lill thought he should have come out and said it. I know that Andrew said later that he came out and said it, but I doubt it. He is too much of a lawyer not to be as vague as possible.
You have to remember that more time than we see passes in between events on the show. They were both functioning on very little sleep and very little food. As anyone who has had an infant knows, you become incredibly forgetful and your memory becomes foggy with lack of sleep. Compounded with the lack of food, I would be surprised if either of them could recall their exact words.
We only know what we were shown. Perhaps Andrew had a conversation with her and perhaps he didn't.