Answer: "Wouldn't It Be Nice" by The Beach Boys
The song was Lucy's father's and mother's song. When her father and her brother, Doug, would go fishing, she would give her father a CD with the song on it so that he would constantly think of her mother and hurry home to see them. Lucy's father told Henry that everyday she met him, she would sing it and they would know. Later in the movie, before Henry began his trip to Alaska, Lucy's father gave him The Beach Boy's CD to listen to. While on his way to Alaska, Henry realized that it was a sign from her father saying that Lucy remembered Henry.