One Whole and Perfect Day is packed with abandoned children. Pop has rejected Lonnie, Clara feels cast out by her father, Rose's parents died when she was young, and even Lily feels like her mother's preoccupation with work resigns her to a life of domestic servitude. Regardless of how tough these situations might be, though, nobody has it harder than Lucy, the girl in black who frequents the trains around their region of Australia looking for financial help.
We don't know much about what caused Lucy's situation, only that it had to be pretty bad. "She was so bloody young, this one," Stan observes. "Her face was grubby in the way he remembered Lonnie's being grubby […] There was a cardboard sign hung around her neck, like a child in a primary-school tableau: 'I am sixteen and pregnant […] My first baby is in care and I have no home and family'" (26.7-8). Lucy's life is made even worse by the fact that she can't speak or hear. Her "terrible sounds, thick and guttural" (26.23) greatly disturb Stan, driving him to show compassion on her when no one else will.
In a way, Lucy is a picture of what children like Lonnie and Clara could have been. In spite of their disagreements, both of them still have family members who love and support them—by contrast, Lucy has nobody. Her situation brings home to Stan the reality of what his strained relationship with Lonnie could cost:
If things went wrong, [Lonnie] knew they were there; he knew, whatever the quarrels, that they'd help him out. Sure he knew. He should know, anyway. (26.28)
The doubt in this statement, though, shows that Stan isn't really sure that Lonnie does know this. Meeting Lucy provides Stan with motivation to make up with his grandson and change his rigid, judgmental ways. It's a bummer for her, but at least in the end it seems that she's been brought into the Samson family fold. And hey—if nothing else, this means Lily will at least take care of her.