Begin by preheating your oven to 350°F (176°C). Line three 8-inch round cake pans with parchment paper, and grease the sides thoroughly.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set this aside for later use.
In a large mixing bowl, cream the butter and sugar on medium speed until you achieve a light, fluffy consistency—about 2-3 minutes. Add in the egg whites and vanilla extract, mixing well until everything is fully incorporated. Make sure to scrape the bowl's sides as needed.
Gradually add the dry ingredients and the wet ingredients (milk, lemon juice, and zest) in alternating stages. Begin with about one-third of the flour mixture, followed by half of the milk and lemon mixture, beating on medium speed until everything is combined. Continue alternating between the dry and wet ingredients, ensuring each addition is well mixed. You should end with the dry ingredients.
Distribute the batter evenly among the three pans. Bake the cakes for 25-30 minutes, checking doneness by inserting a toothpick in the center, which should come out clean. If the tops are slightly browned, this is completely normal.
Allow the cakes to cool in the pans for 1-2 minutes before transferring them to a cooling rack to cool completely.