Preheat oven to 350°F (175°C). Grease a 9x13 inch baking pan or line with parchment paper.
Combine sugar and lemon zest in a large bowl. Rub together with fingers until fragrant and sandy.
Add oil, eggs, lemon juice, and vanilla to sugar mixture. Whisk until smooth and well combined.
Whisk together flour, baking powder, baking soda, and salt in a separate bowl. Gradually add to wet ingredients, stirring just until no flour streaks remain.
Fold in grated zucchini gently but thoroughly. Batter will be thick.
Spread batter evenly into prepared pan, smoothing top with spatula.
Bake 25-30 minutes until edges are golden and toothpick inserted in center comes out clean or with few moist crumbs.
Cool completely in pan before glazing.
Make glaze: Whisk powdered sugar, 3 tablespoons lemon juice, and optional zest until smooth. Add more juice if needed for pourable consistency. Drizzle over cooled bars.