Preheat your oven to 350°F (175°C) and prepare two 9-inch round cake pans by greasing and dusting with flour.
In a large mixing bowl, whisk together the dry ingredients: flour, sugar, baking powder, and salt.
Add softened butter and milk to the dry mixture and beat on medium speed for 2 minutes until smooth.
Add eggs, lemon zest, vanilla extract, lemon juice, and baking soda, and mix on medium speed for another 2 minutes.
Gradually combine the wet mixture with the dry ingredients, mixing on low speed until just combined.
Divide the batter evenly between the prepared pans and bake for 25-30 minutes, checking for doneness with a toothpick.
While the cakes are baking, prepare the frosting by beating cream cheese and butter until creamy, then gradually add powdered sugar, lemon juice, and lemon zest.
Once the cakes are cooled, frost the top and sides with the cream cheese frosting and chill for 30 minutes before serving.