Preheat oven to 325 degrees F. Grease and flour two 8 x 4 inch loaf pans and set aside.
In a large bowl, whisk together the flour, salt, baking powder, and baking soda. Set aside.
In a large bowl, combine sugar and lemon zest. Rub together with your fingers until fragrant.
Add the eggs, olive oil, lemon juice, vanilla to the lemon sugar mixture and stir until smooth. Add in the dry ingredients and stir until just combined, the batter will be thick. Stir in the zucchini and pour the batter into the prepared loaf pans.
Bake for 60-65 minutes, or until tester inserted in the center comes out clean.
Place the loaves on a cooling rack and let cool for 15 minutes in the pans. Loosen the sides of the bread with a knife. Carefully remove the loaves from the pans. Let cool completely on rack.
While the bread is cooling, make the lemon glaze. In a small bowl, combine powdered sugar and lemon juice. Whisk until smooth. Drizzle the glaze over the loaves. Slice and serve.