Preheat the oven to 350°F/180°C. Line 3 6-inch cake pans with parchment rounds and set aside.
In a medium bowl, rub the sugar and lemon zest together with your fingers.
300 grams granulated sugar, 3 tablespoon lemon zest
Pour the lemon sugar, flour, baking powder, baking soda, and salt into the bowl of a stand mixer with the paddle attachment. Mix until combined.
300 grams cake flour, 1 ½ teaspoon baking powder, ⅜ teaspoon baking soda, ½ teaspoon salt
Mix in the softened butter until it looks like wet sand.
113 grams unsalted butter
Add the oil, eggs, and vanilla extract to the bowl. Mix on low until a batter starts to come together.
113 grams vegetable oil, 3 large eggs, 1 tablespoon vanilla extract
Mix in the buttermilk and lemon juice on low until the batter is smooth and well combined.
120 grams buttermilk, 120 grams lemon juice
Distribute the batter between the 3 prepared pans.
Bake for 25-30 minutes until a toothpick inserted in the center comes out clean. Let the cakes cool in the pans for 20 minutes, then flip onto a wire cooling rack and let cool completely.