Preheat the oven to 375 degrees F (190 degrees C). Grease and flour two 9-inch round cake pans.

Mix together cake flour, lemon zest, baking powder, and salt.

Beat egg whites in a glass, metal, or ceramic bowl until foamy. Gradually add 1/3 cup sugar, continuing to beat until soft peaks form.

Cream butter and 1 cup sugar in a large bowl with an electric mixer. Add the flour mixture in batches, alternating with milk and lemon juice, beating batter briefly after each addition. Add lemon extract and egg whites; beat to incorporate into batter. Pour into the prepared cake pans.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 30 minutes. Let cool completely on wire racks before frosting.