One distinct way in which Sam's relationship with Lucy is a healthy one is the open way she is able to communicate with her father.  For example, the relationship that both of them share is open enough for her to ask him, "Daddy, did God mean for you to be like this, or was it an accident?"  If both father and daughter did not have an open relationship, she could not have the ability to ask such a question.  It is disarmingly direct and reflective of an open relationship where the ethics of love and trust have supplanted mistrust and fear.  

A further testament to the openness and healthy nature of their relationship is seen in the exchange about Lucy reading.  She protests at one point, "I don't want to read if you can't."  However, Sam's response is reflective of care and compassion: "No, because it makes me happy! It makes me happy hearing you read. Yeah, it makes me happy when you're reading."  The idea that he can be made happy by virtue of what she is doing suggests an open relationship.  It reflects a healthy one where there is not envy or resentment. Sam is aware that Lucy is smarter than he is.  However, he does not project his own bitterness upon her.  Rather, he is happy for her.  For her part, Lucy is able to recognize that she is "lucky" to have Sam as a father.  She says this in reference to how he takes care of her: "It's ok, daddy. It's ok. Don't be sorry. I'm lucky. Nobody else's daddy ever comes to the park."  The relationship between Sam and Lucy is shown to be a healthy one because both have an intrinsic and mutual respect for one another, supplanting negative emotions and destructive affective displays.