Spray a 9x5" with non stick cooking spray. (I like to use Baker's Joy.) Preheat oven to 325 degrees.
Whisk together oil, sugar, lemon zest, lemon juice, and eggs in a large mixing bowl, then stir in the zucchini.
In a small bowl, whisk together the flour, salt, baking soda, and baking powder. Gently stir into the wet ingredients just until moistened.
Pour batter into prepared pan. Bake at 325° for about 60 minutes, or until a toothpick inserted in the middle comes out clean.
Cool bread in pan for about 10 minutes, then remove to a cooling rack.
For icing, whisk powdered sugar and lemon juice together in a small bowl until smooth. You may need more or less lemon juice to get the right consistency. Drizzle or spread over the top of the loaf.