Preheat the oven to 350°F. Grease a 9x5-inch loaf pan or line with parchment paper and spray with non-stick spray.
Melt the butter: In a large microwave-safe bowl, melt 1/4 cup unsalted butter (about 10–20 seconds in the microwave).
Mix wet ingredients: To the melted butter, stir in 1/2 cup packed brown sugar and 1/2 cup granulated sugar until smooth. Add 1 large egg, 1 teaspoon vanilla extract, 2 tablespoons buttermilk, the zest of 3 lemons, and the juice of 2 lemons. Mix until fully combined.
Add dry ingredients: Stir in 1 3/4 cups all-purpose flour, 1 teaspoon baking powder, 1/2 teaspoon baking soda, and 1/2 teaspoon salt until just incorporated—do not overmix.
Fold in the zucchini: Gently stir in 1 cup shredded zucchini until evenly distributed throughout the batter.
Bake: Pour the batter into the prepared loaf pan and spread it evenly. Bake for 40–50 minutes, or until a toothpick inserted into the center comes out clean.
Cool: Let the bread cool in the pan for 10–15 minutes, then transfer to a wire rack to cool completely before glazing.
Make the glaze: In a small bowl, whisk together the juice of 1 lemon with 1/2 to 3/4 cup powdered sugar, depending on how thick you like your glaze. Drizzle over the cooled bread.