Whisk dry ingredients: Whisk together 2 cups all-purpose flour, 1 teaspoons baking powder, 1 teaspoons baking soda, and 0.5 teaspoons salt in a bowl and set aside.

Combine wet ingredients: In a large bowl, combine 0.5 cups unsalted butter, softened (for cake), 0.5 cups olive oil, 0.8 cups granulated sugar, 0.5 cups brown sugar, 3 large eggs, 1 teaspoons vanilla extract, 2 lemons, zested (for cake), and 0.3 cups fresh lemon juice (for cake).

Add dry to wet: Add the dry ingredient mixture into the wet ingredients and stir until combined.

Fold in zucchini: Gently fold in 3 cups grated zucchini (not drained), without draining the excess water.

Spread batter in pan: Spread the batter evenly into a prepared, parchment-lined baking pan.

Bake: Bake until golden and a tester inserted in the center comes out clean.

Whip frosting: In a stand mixer, whip 0.5 cups unsalted butter, softened (for frosting), 3 cups powdered sugar (for frosting), 2 tablespoons fresh lemon juice (for frosting), 1 lemon, zested (for frosting), and 1 pinch of salt (for frosting) until light and fluffy.

Frost and serve: Once the cake is completely cooled, spread the frosting evenly over the top and serve.