The dusk, or twilight, and the cake of soap contribute to the lesson of Saki's "Dusk" in two ways:

1.  Both the dusk,"the hour of the defeated" and the cake of soap are symbolic of Norman Grotsby's judgmental character.  For, as he sits on the bench in Hyde Park next to the older gentleman "with a drooping air of defiance," Grotsby presumes that he is one who

belonged unmistakably to that forlorn orchestra to whose piping no one dances; he was one of the world's lamenters who induce no responsive weeping.

And, thus, Grotsby dismisses him as a man who returns to a room where he is ignored and considered valueless. Then, as the bench is soon occupied by a young man who puts Grotsby on his guard with his story of having gone out to buy soap and then could not find his way to the room because he had switched hotels. Priding himself in his logic, Grotsby responds to the young man's suggestion that he needs money for lodging,

"the weak point of your story is that you can't produce the soap....To lose an hotel and a cake of soap on one afternoon suggests willful carelessness..."

But, after the young man leaves angrily, Grotsby believes that he finds the soap under question, hurries to give the youth credit for his story, and lends him money.  Upon his return, Grotsby feels pride in his judiciousness while mildly scolding himself, 

It's a lesson to me not to be too clever in judging by circumstances."

2. Of course, the dusk and the cake of soap also contribute to the irony of the story as Grotsby's mistakes in judgment would not have occurred if he had earlier seen the cake in the dusk and if he had been better able to judge the young man's character. Indeed, Grotsby is right in counting "himself among the defeated."