What is the irony in Saki's short story "The Lumber Room"?

The irony of Saki's "The Lumber Room" is in the twists of events. Instead of the self-appointed aunt being successful in punishing Nicholas and rewarding the other children by sending them to the beach, events turn out the other way around. For it is the two who go to the beach and the aunt who spend a miserable day, while Nicholas delights in the lumber room while leading the aunt to believe that he wants to enter the gooseberry garden.

Because Nicholas has tricked his aunt with his declaration that there was a frog in his bowl of bread-and-milk, which has elicited her adamant denial in which she is embarrassingly proved in error, the aunt punishes him for his subversion of her authority: He must remain home while his cousins go to Jagborough sands that afternoon. Even though the girl-cousin scrapes her knee and cries, the aunt informs him that "it will be a glorious afternoon for racing about over those beautiful sands. How they will enjoy themselves!"

In the meantime, Nicholas is to remain home, where he is restricted from entering the gooseberry garden. When Nicholas looks at her with an expression of obstinacy, she becomes determined to watch him. Because "[S]he was a woman of few ideas, with immense powers of concentration," the aunt works for awhile in the garden so that she can keep an eye on both entries. Nicholas makes a show of trying to enter the garden, knowing that she will guard it assiduously now.

In the meantime he sneaks away, and he "rapidly executes a plan of action that had long germinated in his brain": Nicholas has discovered the key to the lumber room above its door. Now, he opens this room and delights in his deception and in his opportunity to engage his mind in flights of fancy and his eyes with wondrous things. For instance, there is a tapestry that generates a story in Nicholas's mind, as well as quaint candlesticks and a teapot shaped like a duck whose bill is the pour spout, unlike the shapeless one the aunt uses for the children. Further, Nicholas discovers a wonderful book of beautiful birds.

Suddenly, 

...the voice of his aunt in shrill vociferation of his name came from the gooseberry garden without.

Nicholas hurriedly closes the book and replaces it. His aunt has taken a sadistic delight in Nicholas's absence, certain that she will catch him in the gooseberry garden. However, she has had an accident and is heard shrieking. Nicholas carefully closes the door, locking it and replacing the key. He saunters to the garden wall, where his aunt calls out to get the ladder because she has fallen into an empty rain water tank whose sides are too slippery for her to get any footing to climb out. "I was told I wasn't to go into the gooseberry garden," Nicholas tells her victoriously, and pretends that he believes her voice that of the devil sent to tempt him. He walks away in triumph, and a maid later finds her.

"Tea that evening was partaken of in a fearsome silence" not only because of the aunt's humiliation in the garden, but also because the boy and girl who were "rewarded" with the trip to the beach have spent a miserable day. For the tide was so high that there was no sand to play in, and Bobby's boots were so tight that he was in pain the entire time. Also, the aunt maintained a "frozen muteness," having spent thirty-five minutes in a rain tank. Despite their misfortunes, Nicholas re-absorbs himself in the tale he has created about the huntsman on the tapestry.

What is the irony in Saki's short story "The Lumber Room"?

I think that the irony of this story is that the child who was to be punished (Nicholas) had the best day, the most fun.  Meanwhile, the children who were supposed to be having the fun did not.  So Nicholas ends up being rewarded for his bad deeds.

The theme of the story, I think, is the idea that adults are not always very intelligent when dealing with children.  Nicholas's aunt tells him that there can't possibly be a frog in his food when there actually is one.  She tells him she knows he's in the gooseberry garden when he isn't.  She tells him there's no strawberry jam when really there was some.

So the story shows adults being too certain and not believing the kids.  And it shows adults trying too hard to impose discipline.  And it shows adults telling falsehoods to try to control the children.  All of these together point out that adults err when they try to have too much control and when they do not take their children seriously.

How does Saki's "The Lumber Room" humorously represent a serious theme?

"The Lumber Room," like Saki's "Open Window" is a little more lighthearted than his darker tales such as "The Interlopers." At first glance, "The Lumber Room" seems to be about a clever boy who outwits his aunt.  However, the story does touch on issues such as a boy's desire to explore and to do exactly what his authority figure has told him not to do.  Moreover, Saki uses Nicholas, the main character, to warn adults to be careful of using scare tactics, disciplining out of anger, or of lying to children. Nicholas's aunt constantly makes threats, most of which seem only to entice Nicholas to test them; she also disciplines Nicholas out of frustration and anger rather than really trying correct his behavior, and Nicholas catches her in a lie which he readily connects to "The Evil One," leaving his aunt no viable explanation of her own behavior.

Overall, the story's tone is humorous, and Saki does not portray any violent injuries or deaths, but for any adult reading the story, the author is able to stress the importance of being careful what you say to ever-observant children.