Preheat the oven to 350 degrees F. Line two 12-cup muffin pans with paper liners.
Make the cupcakes: Whisk the flour, baking powder and salt in a medium bowl. Combine the olive oil and sugar in a large bowl and beat with a mixer on medium-high speed until smooth and creamy, about 4 minutes. Beat in the eggs, one at a time, then beat in the vanilla and lemon zest. Reduce the speed to low; beat in the flour mixture in three batches, alternating with the milk. Increase the speed to medium high and beat until combined.
Divide the batter among the muffin cups, filling them three-quarters of the way. Bake until the tops are lightly golden and a toothpick inserted into the centers comes out clean, 20 to 25 minutes. Let cool 10 minutes in the pan, then remove to a rack to cool completely.
Meanwhile, make the frosting: Combine the egg whites and sugar in the bowl of a stand mixer and place over a small pot of simmering water (make sure the bottom of the bowl does not touch the water). Whisk by hand until the sugar is dissolved and the mixture is warm to the touch, about 5 minutes. Remove the bowl from the pot and attach to the mixer; beat with the whisk attachment on high speed until the meringue is shiny and holds stiff peaks, about 7 minutes. Switch to the paddle attachment. With the mixer on medium speed, gradually add the butter and beat until smooth, 1 more minute. Add the vanilla and mix until just combined. Spread the frosting on the cupcakes.
Photograph by Linda Xiao