Preheat the oven to 350°F, or 175°C. Grease a 9×13-inch baking pan and line it with parchment paper.
Wash and finely grate the zucchini. If it is very watery, gently squeeze out some excess moisture, but do not dry it completely.
In a large mixing bowl, whisk together the granulated sugar, vegetable oil, eggs, lemon zest, lemon juice, and vanilla extract until smooth.
In a separate bowl, whisk together the flour, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients. Stir gently until just combined.
Fold the grated zucchini into the batter. Avoid overmixing, as this can make the bars dense.
Pour the batter into the prepared baking pan and spread it evenly.
Bake for 25–30 minutes, or until the top is lightly golden and a toothpick inserted in the center comes out clean or with a few moist crumbs.
Remove the pan from the oven and place it on a cooling rack. Allow the bars to cool completely before adding the glaze.
To make the glaze, whisk the powdered sugar with 2 tablespoons of lemon juice until smooth. Add more lemon juice gradually if needed.
Spread or drizzle the lemon glaze over the cooled zucchini bars.
Let the glaze set for 15–20 minutes, then cut the dessert into 24 squares and serve.