The doll's house given to the Burnell daughters is incredibly detailed, with lots of little objects that delight the girls and make the house seem even more special. Kezia, though, prefers a tiny lamp the best of all these details. It is a "little amber lamp with a white globe" that is filled with a liquid that looks like oil. The lamp is so realistic, despite its tiny size, that it even seems as though one could light it (though one cannot because it is a toy). Some of the dolls meant to go inside are stiff or too big, but the "lamp was perfect" to Kezia. When the Burnells go to school, Isabel—Kezia's oldest sister—forgets to tell the other girls about the lamp, and Kezia reminds her. To Kezia's mind, "Isabel wasn't making half enough of the lamp," because Kezia thinks it is so special and perfect.
After all the other girls in class have seen the doll house, and the lamp, Kezia invites the oft-excluded Kelvey girls to come see it. They are the only ones who have not been invited because they are poor. We learn that their mother cleans and does laundry for a living, and their father is probably in jail. Kezia's older sisters Isabel and Lottie are upstairs and not present to stop Kezia from including Lil and Else in the experience that everyone else has shared. Although the horrid Aunt Beryl banishes the Kelveys from the yard, Else soon forgets "the cross lady" and says softly, "I seen the little lamp." In the end, the lamp is what matters to her.
Therefore, I think we can interpret the lamp in a couple of ways: first, it symbolizes the innocence of childhood. Isabel and Lottie have already begun to be affected by the warped values of adults like their mother and Aunt Beryl, though Kezia and the Kelveys have not. The younger children still possess this innocence and are the only ones who truly appreciate the lamp's beauty. We might also interpret the lamp as a symbol of inclusion. Kezia is kinder than her older sisters, and she extends compassion by including the Kelveys when others seek to exclude them just to be cruel.