Preheat the Oven: Start by preheating your oven to 350°F (180°C). Grease and flour two round cake pans.
Mix the Dry Ingredients: In a large bowl, combine the cake flour, baking powder, baking soda, and salt, and set aside.
Cream Butter and Sugar: In another bowl, beat the butter and sugar together until light and fluffy.
Add Eggs and Vanilla: Gradually add the eggs, one at a time, mixing well after each addition. Stir in the vanilla extract.
Mix Wet Ingredients: In a separate bowl, combine the Greek yogurt, lemon juice, and lemon zest.
Combine Everything: Gradually mix the dry flour mixture and the yogurt mixture into the butter mixture, alternating between the two until fully combined.
Bake the Cake: Divide the batter evenly between the two prepared cake pans and bake for 25-30 minutes or until a toothpick comes out clean.
Cool the Cakes: Allow the cakes to cool in the pans for about 10 minutes before transferring them to a wire rack to cool completely.
Prepare the Frosting: While the cakes cool, beat together the cream cheese and butter until creamy. Gradually add the powdered sugar, lemon juice, lemon zest, and vanilla extract, mixing until smooth and fluffy.
Frost the Cake: Once the cakes are cool, place one layer on a serving plate and spread a generous amount of frosting on top. Place the second layer on top and frost the top and sides of the cake.