Preheat your oven to 350°F (175°C) and grease a 9x13-inch baking pan.

In a large bowl, whisk together the flour, lemon pudding mix, baking powder, baking soda, and salt. Set aside.

In another large bowl, beat the butter, oil, eggs and sugar together until light and fluffy. Stir in the buttermilk, vanilla extract, lemon juice, and lemon zest.

Add the dry ingredients to the wet mixture, mix until just combined.

Pour the batter into the prepared baking pan and spread evenly. Bake for 25–28 minutes, or until a toothpick inserted in the center comes out clean. Let the cake cool completely in the pan.

To make the frosting, beat the softened cream cheese and butter together until smooth and creamy. Gradually add the powdered sugar, mixing until fluffy. Stir in the lemon juice and lemon zest.

Spread the frosting evenly over the cooled cake. For topping, spoon small dollops of lemon curd across the top and gently swirl if desired. Finish with a sprinkle of fresh lemon zest.

Chill slightly before serving for cleaner slices, or enjoy at room temperature.