Preheat oven to 350° F. Butter two 6-inch cake pans and line bottoms with rounds of parchment.
In the bowl of a stand mixer fitted with the paddle attachment, combine sugar, lemon zest, and juice; mix for a minute or so, until fully incorporated.
Pour in flour, baking powder, and salt and mix until well combined.
Add butter; beat until butter breaks down into small pea-sized pieces, 2-3 minutes.
Whisk together egg whites, milk, and vanilla. Add all but 1/4 cup of milk mixture to butter mixture and beat on medium speed until thick and creamy, 2-3 minutes. With mixer on low, gradually pour in remaining milk.
Divide batter evenly among prepared pans. Bake until toothpick inserted in center comes out clean, about 20-25 minutes. Allow to cool completely.