1. Preheat the oven to 350°F. Grease three 8-inch round cake pans, line the bottoms with parchment paper, and lightly flour the sides.

2. In a medium bowl, whisk together the flour, baking powder, baking soda, and salt.

3. In a large bowl, rub the lemon zest into the granulated sugar with your fingertips until fragrant.

4. Add the softened butter and oil to the lemon sugar. Beat until pale, creamy, and fluffy.

5. Beat in the eggs one at a time, then mix in the lemon juice and vanilla extract.

6. Add the dry ingredients in three additions, alternating with the buttermilk. Mix on low speed just until combined.

7. Divide the batter evenly between the prepared cake pans and smooth the tops.

8. Bake for 22 to 26 minutes, or until a toothpick inserted in the center comes out clean or with a few moist crumbs.

9. Cool the cakes in the pans for 10 minutes, then transfer them to wire racks to cool completely.

10. For the frosting, beat the softened butter until creamy. Gradually add powdered sugar, then mix in lemon juice, lemon zest, vanilla, salt, and heavy cream. Beat until fluffy.

11. Place one cake layer on a serving plate. Spread frosting over the top, add the second layer, and repeat. Add the final layer.

12. Apply a thin crumb coat, chill briefly, then frost the top and sides with the remaining lemon buttercream.

13. Decorate with lemon zest, lemon slices, or buttercream swirls before serving.