Preheat oven to 350°F (175°C). Grease two 8-inch round cake pans and line the bottoms with parchment. Whisk flour, baking powder, baking soda, and salt in a medium bowl.

Beat butter, sugar, and oil together with a hand or stand mixer on medium speed for 3 minutes until pale and smooth.

Add eggs one at a time, beating after each. Mix in lemon zest, lemon juice, and vanilla. On low speed, alternate adding the flour mixture and buttermilk, starting and ending with flour. Mix just until combined.

Divide batter between pans. Bake 28–32 minutes until a toothpick comes out with moist crumbs. Cool in pans 10 minutes, then turn out onto a wire rack to cool completely.

For the frosting, beat cream cheese and butter until smooth. Gradually add powdered sugar, then add lemon zest, vanilla, and salt. Beat on high for 2 minutes until light and fluffy.

Place one cake layer on a plate, spread with frosting, top with second layer. Frost top and sides. Garnish with extra lemon zest if you like. Slice and serve.