I think the idea that Henry wrote the book that Lucy was holding when she went to visit him makes a lot of sense. That could be why it had that weird white cover. It definitely wasn’t a storybook and we know that all the storybooks look the same. That means that there is probably something else going on here.
It is so weird because the guy in the first scene with the girl acts so different then the guy. I keep wondering if it is even the same person.