Preheat oven to 325 degrees and lightly grease one 9x5 loaf pan.
In a large bowl, gently stir sugar and lemon zest together. Add egg, vegetable oil, and vanilla to sugar mixture and whisk to combine. Once fully combined, stir in zucchini. In a separate bowl, whisk together flour, salt, baking soda, baking powder, and cinnamon. Stir the flour mixture into the zucchini mixture until just combined. Pour into prepared loaf pan.
Bake 50-55 minutes or until a toothpick inserted in the center of the bread comes out clean. Move pan to wire rack and cool in pan for 10 minutes before turning out onto a wire rack to finish cooling completely.
In a medium bowl, whisk together the powdered sugar, lemon juice, and vanilla. Once bread is cooled, drizzle the glaze over the bread.