I think we probably need to remember that we've only seen a few hours of the time they were there. Lillie won't know what has been edited in/out and so it is far less likely that she'd lie to the extent you're all making out knowing that the public could know she's lying. I definitely remember her saying he'd cuddled her on the first night, for example.
I don't think she lied to Millie. I think we just didn't see the extent of his behaviour during the 3-4 hours of TV we were shown. They couldn't have filmed/showed every conversation and all throughout the night.