What does the lamp symbolize in this story?
The rich Burnell children receive a gift of a "perfect" doll house, with papered walls, carpet, furniture, just the most amazing thing one has ever seen. The people in it, though, the dolls, are stiff and look like they do not belong. That is because the upper class society that the house represents is stiff. The snobbery of class structure "stinks" - and that is why there is a smell to the house. The people and the smell are two negative things about the house.
The best thing about the house is the little lamp.
But what Kezia liked more than anything, what she liked frightfully, was the lamp. It stood in the middle of the dining-room table, an exquisite little amber lamp with a white globe.
The lamp is tiny, because there is a "tiny" bit of human kindness showing through the ostentatious house. Nevertheless, the one person who shows kindness in this story, Kezia, notices the lamp right away and decides that it is the best part of the house. When the poor Kelvey girls are allowed to view the house, the youngest child ends the story by saying "I seen the lamp." This means that she saw the kindness, even for just a brief moment.
Read about the story here on eNotes.