Preheat the oven to 350°F (175°C). Line the bottom of a 5 x 9-inch loaf pan with parchment paper and lightly grease with non-stick spray.
In a medium bowl, whisk together the flour, lemon pudding mix, baking powder, baking soda, and salt.
In a 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 smooth and well combined.
Gradually add the dry ingredients to the wet mixture, mixing until just incorporated. Stir in the lemon zest.
Pour the batter into the prepared loaf pan and bake for 55 minutes, or until a toothpick inserted in the center comes out clean.
Allow the loaf to cool in the pan for 5–10 minutes. Run a knife around the edges, then transfer the loaf to a wire rack to cool completely.
For the frosting, beat together the softened butter, lemon juice, and lemon extract. Gradually add the powdered sugar and mix until smooth and creamy.
Spread the frosting evenly over the cooled loaf. Refrigerate for at least 30 minutes to set before slicing and serving.