Preheat oven to 350°F (175°C). Grease or line a 9×13-inch baking pan.
Place grated zucchini in a clean kitchen towel and squeeze firmly to remove as much liquid as possible.
In a large bowl, whisk sugar, oil, and eggs until smooth, then mix in lemon juice, lemon zest, and vanilla.
In a separate bowl, whisk flour, baking powder, baking soda, and salt.
Add dry ingredients to wet ingredients and stir gently until just combined.
Fold in the drained zucchini, mixing only until incorporated.
Spread batter evenly into the prepared pan.
Bake for 30–35 minutes, until lightly golden and a toothpick inserted in the center comes out clean.
While bars are cooling slightly, whisk powdered sugar with lemon juice until smooth and pourable, then stir in zest if using.
Pour glaze over warm (not hot) bars and spread gently.
Let glaze set for 15–20 minutes before slicing.