Prepare the oven and pan: Preheat the oven to 350°F (175°C). Line the bottom of a 5 x 9-inch loaf pan with parchment paper. Lightly grease the pan and parchment with non-stick baking spray.
Mix dry ingredients: In a bowl, whisk together the flour, pudding mix, baking powder, baking soda, and salt.
Mix wet ingredients: In a separate large bowl, use a hand or stand mixer to beat the eggs, sugar, butter, vanilla extract, lemon extract, lemon juice, oil, and Greek yogurt until well combined.
Combine wet and dry: Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Stir in the lemon zest.
Bake the loaf: Pour the batter into the prepared loaf pan. Bake for 55 minutes, or until a toothpick inserted into the center comes out clean.
Cool the loaf: Let the cake cool in the pan for 5-10 minutes. Run a knife around the edges, then remove the loaf from the pan and place it on a wire rack to cool completely.
Prepare the frosting: In a bowl, beat the butter, lemon juice, and lemon extract with a mixer. Gradually add the powdered sugar, beating until smooth and creamy.
Frost and serve: Spread the frosting evenly over the cooled loaf. Refrigerate for at least 30 minutes to set the frosting before slicing.