Paul’s mother realizes that if she had luck she would have money and would thus be happier.
The mother is very selfish, and feels that she deserves more than she has. Money will make her happy. She is described at the beginning of the story as having “no luck.”
Young Paul asks his mother if money is the same as luck.
"No, Paul. Not quite. It's what causes you to have money."
"Oh!" said Paul vaguely. "I thought when Uncle Oscar said filthy lucker, it meant money."
"Filthy lucre does mean money," said the mother, "But it's lucre, not luck."
She tells him that if you are lucky you have money. Paul's understanding of the world is very limited. He just wants to make his mother happy. She can't be happy, and has no interest in anyone else's happiness. In her selfishness, she fails to see what her persuit of luck and money is doing to her son. This ultimately leads to his destruction.