Preheat the oven to 350°F (175°C). Grease and flour a 9×5-inch loaf pan and set aside.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, salt, and grated lemon zest.
In a large bowl, beat the granulated sugar, light brown sugar, and eggs together until smooth and creamy.
Add the vegetable oil, Greek yogurt, vanilla extract, and lemon juice to the sugar and egg mixture. Beat until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing just until combined.
Fold in the grated zucchini, ensuring it is evenly distributed throughout the batter.
Pour the batter into the prepared loaf pan and smooth the top with a spatula.
Bake for 50 to 55 minutes, or until a toothpick inserted into the center comes out clean.
Remove the loaf from the oven and let it cool in the pan for 15 minutes.
Transfer the loaf to a wire rack to cool completely.
Optional: To make the lemon glaze, whisk together the powdered sugar and lemon juice until smooth. Drizzle over the cooled loaf before serving.