Preheat the oven to 375 degrees F. Butter and flour an 8.5 by 4.5-inch loaf pan.
In a medium bowl, whisk together the flour, baking soda, salt, and baking powder.
In a separate large bowl, whisk together the sugar, oil, eggs, lemon zest, lemon juice, and vanilla. Whisk in the shredded zucchini.
Add the dry ingredients to the wet ingredients and stir to combine, being careful not to over-mix.
Pour the batter into the prepared pan. Bake until the loaf is golden and a toothpick inserted in the center comes out clean or with just a couple crumbs, about 45 to 60 minutes. (Start with 45, check and add more time, as needed). Let the bread cool completely before icing.
ADD THE ICING:
In a medium bowl, whisk together all ingredients for the icing, adding water 1 teaspoon at a time if needed to achieve the desired consistency.
Place the bread on a wire rack and drizzle the icing on the bread and let it set before slicing.
Notes
Unless the zucchini is extremely wet, there’s no need to wring out the moisture.