Preheat oven to 350°F. Grease an 8×4-inch or 9×5-inch loaf pan with nonstick cooking spray or butter.
Add oil, both sugars, eggs, lemon juice, lemon zest, and vanilla extract to a large bowl. Stir until smooth.
Mix in baking soda, baking powder and salt.
Stir in flour, mixture will be thick. Add zucchini and stir until combined – mixture will get looser and more pourable after stirring in zucchini.
Pour batter into prepared pan. Bake 50-60 minutes (9×5-inch pan) or 55-65 minutes (8×4-inch) pan, or until a toothpick comes out clean from the center of the loaf.
Cool before adding glaze.
To make glaze: whisk powdered sugar and 1 tablespoon lemon juice, adding more as needed for desired consistency. Drizzle over bread.
Store covered for up to 2 days or freeze for up to 3 months.