Preheat the oven to 350°F. Line a loaf pan with parchment paper, leaving overhang on the two long sides.
Prep the zucchini: Grate the zucchini on the large holes of a box grater. Transfer to a small bowl and toss with 2 tablespoons of the sugar. Set aside for 10 minutes.
Mix the dry ingredients: In a medium bowl, whisk together the flour, baking powder, baking soda, and salt.
Mix the wet ingredients: In a large bowl, whisk the remaining sugar with the eggs until pale and thickened, about 1 minute. Add the oil, milk, lemon zest, lemon juice, and vanilla. Whisk until smooth and emulsified.
Combine: Pour the dry ingredients into the wet. Fold gently with a rubber spatula until no streaks of flour remain. A few lumps are fine.
Add the zucchini: The zucchini will have released liquid – don't drain it. Add the zucchini and its liquid to the batter. Fold just to distribute.
Fill the pan: Scrape the batter into the prepared pan. Sprinkle the turbinado sugar evenly over the top.
Bake: Bake for 55–65 minutes, or until a toothpick inserted in the center comes out with only a few moist crumbs. If the top is browning too fast at 45 minutes, tent loosely with foil.
Cool: Let the loaf cool in the pan for 15 minutes, then lift it out using the parchment and transfer to a wire rack. Cool completely before slicing.