What do you think Saki is trying to show about the nature of children and adults in Lumber Room?

Your question is asking you to form an opinion based on the text of the story. In “The Lumber Room” by Saki, the author is trying to demonstrate how adults often believe they are wiser than children based solely upon their age, not their intellect.
Saki creates a witty, cunning, intellectual character as she develops the protagonist, Nicholas. Even as a child, he has the ability to outsmart the adults in his family.
While sitting at the breakfast table, Nicholas claims there is a frog in his milk and bread. The adults assure him this is an impossibility until he produces the frog, which he placed there himself. Saki is demonstrating how adults often refuse to listen to children when something seems implausible.
One of the adults attempts to impose her authoritarian ways upon Nicholas but he is able to outsmart her a number of times. He is also able to prove that she does not listen when the other children are talking. He explains why the beach trip he is being excluded from will be a disaster based on what the other children said. Unfortunately, the aunt was so caught up in her anger and intent to punish Nicholas that she did not hear what they said.
In general, Saki is demonstrating the nature of adults to feel superior and wiser than children. They consider themselves to be authority figures. It is the nature of children to test their limits with authority figures, and many of them have valid reasons for doing so.