You will of course need to expand the brief analysis of the theme of these two fascinating stories by unpacking the style of the author in conveying the message.
"The Rocking Horse Winner" is clearly a fable about greed and in particular its dangers. The mother in the tale is consumed by greed, to the point where it alienates her from her children and her son is driven to desperate lengths to help his mother. It is important to note that even the temporary relief provided by Paul's "winnings" only serves to augment the sense of greed and the voices in the house that drives the children wild. In the end, in this didactic short story, D. H. Lawrence shows us the danger of greed by allowing the mother to gain the wealth she desires, but only at the expense of the death of her son.
In "The Lottery", one...
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of the central themes of the story is the violence and cruelty inherent in even the most civilised of societies. A big part of the message of this story is conveyed by the twist of the tale only revealed at the end - we never find out the "prize" of the lottery until the very end, where the chilling significance of the piles of stones made by children at the beginning is brought home. Even the most advanced societies are able to commit and perpetrate hideous acts against one of their own, even an innocent member, and linked to this is the inability of the group depicted in the story to stand up as individuals and protest against the violence. In the end, all participate in the grim act of violence that brings the tale to its close.
What is significant about the titles "The Rocking-Horse Winner" and "The Lottery"?
The titles of these books give a clue to what the main storyline is about, as all titles usually do. The message of each of these stories is also reflected in the titles. For example, "The Rocking Horse Winner" reflects the message that a child, a small child, on a rocking horse, was able to win something. But it is a bit absurd; how can a rocking horse win anything? How can a child's toy be any part of a serious adult world of money and winning? And, that is one of the messages of the story; a child takes on adult responsibilities and stresses, and "wins" his goal, but in the end, the pressure of trying to be an adult takes his life. So, it is a "winner", but done with a rocking-horse, or a child. And so, we see the absurdity of that entire situation, and how impossible it really is.
For "The Lottery", the title conveys the message of the story that the person chosen to die is chosen in a completely random and impersonal way. When one thinks of a lottery, they think of large odds stacked against their favor, but if they win, it's good luck. In this story though, it is bad luck to win the lottery; it is a reversal of expectations. The lottery is in fact the most important "character" of the story, because a person's life lies in its hands. So, the lottery is not only the title, but the key character, key determinant of human life, and the entire social system around which this society is based. A lottery is impersonal, just as their selection of person is impersonal.
I hope that those thoughts help a bit; I provided links below to further discussion of theme and messages for each story, and those should help too. Good luck!