Place a rack in the center of the oven and preheat the oven to 350 degrees F. Butter and flour two 8x2-inch round cake pans, line with parchment paper, then butter the parchment too.
In a medium bowl, sift together the cake flour, baking powder, and salt. In a separate medium bowl or large measuring cup, whisk together the buttermilk and egg whites until combined.
Place the granulated sugar and lemon zest in the bowl of a standing mixer or a large mixing bowl and rub them together with your fingers until the sugar is moist and fragrant. Add the butter and beat on medium speed for 3 full minutes, until very light and fluffy. Beat in the lemon extract.
Beating on medium speed, add one-third of the flour mixture, then half of the egg/buttermilk mixture and beat until combined. Still beating on medium speed, add the next third of the dry ingredients, then the remaining eggs/buttermilk. Beat until the batter is smooth, then add the remaining dry ingredients. Beat for 2 additional minutes on medium speed, ensuring the batter is very well combined and that plenty of air has been beaten into it.
Divide the batter evenly between the two pans and smooth the tops with a rubber or offset spatula. Bake for 30 to 35 minutes, or until the cakes are well risen, spring back lightly when touched, and a small knife inserted into the center comes out clean.
Place the cake pans on a wire rack and let cool 5 minutes, then run a dull knife around the sides of the cake to loosen. Gently invert the cake into your hand so that it comes out of the pan, remove the paper liner, then place the cake directly back onto the wire rack, bottom (flat) side down and right-side up. Let cool to room temperature.
Prepare the frosting: Using a stand mixer fitted with a paddle attachment or a hand mixer, beat the cream cheese and butter together on medium speed until smooth and no lumps remain, about 3 full minutes. Reduce the mixer speed to low, then add the powdered sugar, 1 tablespoon lemon juice, lemon zest, vanilla extract, and salt. Once the sugar begins to incorporate, increase the mixer to high speed and beat for 3 minutes. Add the remaining tablespoon lemon juice to thin if desired.
Frost the cake: First, using a large serrated knife, trim the tops off the cake layers to create a flat surface. Place 1 layer on your cake plate or stand. Tuck wax or parchment paper strips underneath the edges of the cake to protect the plate. Evenly cover the top with lemon cream cheese frosting. Place the second cake layer on top, cut-side down. Top with more frosting and spread the frosting down around the sides. Decorate as desired. You can slice the cake right away, but for the cleanest cut, refrigerate the frosted cake or place in a cool room for 40 minutes to set. Let the cake come as close to room temperature as possible prior to serving—serving cold can cause some of the fresh lemon flavor to be hard to taste.
*Cake flour is important for this recipe to ensure the layers are extra fluffy and light. If you do not have cake flour, you can make your own by measuring 2 1/2 cups all-purpose flour, removing 5 tablespoons of the measured flour, adding 5 tablespoons of cornstarch, then sifting the mixture together 5 times. Measure out the 2 1/4 c. needed for the recipe, then bake as directed.
To Make Ahead. Bake the cake layers up to 1 day in advance, let them cool completely, then wrap airtight. Store them at room temperature until ready to frost. Frosting can be prepared 1 day in advance and stored in an airtight storage container in the refrigerator.
To Store. Cover the cake, and store it in the refrigerator for up to 2 days. Let it come to room temperature before serving.
To Freeze. Freeze your frosted or unfrosted cake for up to 2 months. Let it thaw overnight in the refrigerator, then bring it to room temperature before serving.