Does the bold part refer to what Lucy said {She said she wouldn’t…} or does it refer to the fact that she tried to shut the door? Some people may disagree with Lucy about what?
She saw she would have to read it standing (and anyway there were no chairs) and also that she would have to stand with her back to the door while she read it. So at once she turned to shut the door.
It wouldn’t shut.
Some people may disagree with Lucy about this, but I think she was quite right. She said she wouldn’t have minded if she could have shut the door, but that it was unpleasant to have to stand in a place like that with an open doorway right behind your back. I should have felt just the same. But there was nothing else to be done.