To make the lemon cake: Preheat the oven to 350°F (180°C). Spray two 9-inch round cake pans with nonstick cooking spray, line the bottom of the pans with parchment paper, and set aside.
In a large mixing bowl, whisk the cake flour, baking powder, baking soda, and salt together until well combined. Set aside.
In a separate large mixing bowl or measuring cup, whisk the buttermilk, oil, lemon juice, and vanilla extract together until well combined. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment or in a large mixing bowl using a handheld mixer, beat the butter on low speed until smooth, then slowly mix in the granulated sugar.
Once all of the sugar is added, add the lemon zest, and increase to medium speed and continue mixing for another 4 to 5 minutes or until the mixture is light and fluffy.
Mix in the eggs, one at a time, make sure to stop and scrape around the bottom and sides of the bowl after each egg.
Add the dry ingredients in three additions alternating with the buttermilk mixture (begin and end with the dry ingredients) on low speed. Mix in each addition until just combined, making sure not to over mix the batter.
Use a rubber spatula to scrape around the bottom and sides of the bowl to ensure that everything is well combined.
Evenly divide the cake batter between the two prepared cake pans and spread it around into one even layer.
Bake for 28 to 32 minutes or until a toothpick inserted into the center of the cakes comes out clean. Remove from the oven and allow to cool in the pans for about 20 minutes. Slide a knife around the outside of the cakes, then carefully remove the cakes from the pans, and transfer to a wire rack to cool completely.
To make the lemon cream cheese frosting: In the bowl of a stand mixer fitted with the paddle or whisk attachment, or in a large mixing bowl using a handheld mixer, beat the cream cheese until smooth. Add the butter and mix for about 30 seconds to 1 minute until well combined and smooth.
Add the powdered sugar and lemon juice (start with 1 tablespoon and add more if needed) and continue mixing until fully combined, stopping to scrape down the sides of the bowl as needed.
To assemble the cake: Level the tops of each cake with a knife or cake leveler. Place one of the cakes on a cake stand, top with a layer of frosting, and smooth it out into one even layer. Place the second layer on top, then use the remaining frosting to frost the top and sides of the cake.