Preheat oven to 325 degrees F. Grease and flour or use baking spray to coat two 8 x 4 inch loaf pans and set aside.
In a large bowl, whisk together the flour, salt, baking powder, and baking soda.
In another large bowl, combine sugar and lemon zest, until fragrant.
Add the eggs, olive oil, apple sauce, lemon juice, and vanilla to the sugar mixture. Mix until smooth. Add the dry ingredients to the wet ingredients and mix just until combined. The batter will be thick.
Stir in the zucchini and pour the batter into the prepared loaf pans.
Bake for 45-60 minutes, or until tester inserted in the center comes out clean. Oven temperatures vary greatly. Be sure to start checking the bread at the 45 minutes mark.
Place the pans on a cooling rack and let cool for 15 minutes. Loosen the sides of the bread with a knife and carefully remove the loaves from the pans. Let cool completely on rack.
Store at room temperature for 3 days or in the refrigerator for up to 1 week.