Concerning theme in "The Rocking-Horse Winner," the enotes Study Guide on the short story lists and explains the following themes:
The obsession with wealth and material items is pitted against the responsibilities of parenting in "The Rocking-Horse Winner." It is the responsibility of the parents to provide for the children in a family. It is also the responsibility of the parents to spend money wisely and budget carefully, so that the bills are paid and no one goes without food, clothing, or shelter. However, in this story, Lawrence turns this on its ear, making the parents complete failures at financial dealings and their son Paul incredibly gifted at making money, albeit by gambling....
Generosity and Greed
The disparity between Paul's generosity and his mother's greed is another theme of "The Rocking-Horse Winner." Paul generously offers all his winnings to the family, in order to relieve the family's dire need for money. He seems to have no needs of his own and is motivated solely by the desire to help his mother. Paul's unselfish generosity is contrasted starkly with the mother's greed and selfishness....
Paul's desire to earn money for the family can be said to be an unconscious desire to take his father's place, a concept that psychoanalyst Sigmund Freud termed the "Oedipus complex." This is a reference to the story from ancient Greece in which Oedipus, who was raised away from his parents, accidently kills his father and marries his mother. Freud suggested that all boys go through a stage where they want to take their father's place, Paul's desire to take care of the family's needs is Oedipal....
Thus, the ideas of responsibility, which the parents don't have and Paul does, greed (the mother) and generosity (Paul), and Paul's desire and need to take his father's place are revealed in the story.
Unfortunately, and ironically, the only worthy character in the story, Paul, the one who takes control and saves the family, is the one who dies. And as he does so, he secures for his mother more money that she could every dream of, although, of course, that probably won't be enough for her, either.
There are several possible themes in this short story. The main theme is that of greed and materialism, and how it can never be satisfied, or bring true happiness or peace. Throughout the entire story, the mother wants more and more money; the more she gets, the more she needs. Does it ever make her happy? No. Paul, her son, equates love with luck and money; he strives the entire story, and essentially sacrifices his life, to get money. It only wears him down and kills him in the end. Greed demands everything and gives only misery in return. That is the most powerful theme in the story.
Other possible themes are love, family, wealth, and happiness. All of these things can be discussed at length and supported through examples in the text. I hope that helps; good luck!