Heat oven to 350°F and line a 9 x 5-inch loaf pan with parchment paper. Spray the parchment with baking spray and set aside.
Combine avocado and eggs in a large bowl and mash with a potato masher until smooth. Whisk in brown sugar and lemon zest.
In a separate medium bowl combine flour, baking powder, and salt. Whisk until incorporated. Dump flour mixture into avocado mixture, add zucchini, and stir with a rubber spatula until moist throughout. Mixture will be very thick.
Scrape into the prepared baking pan and bake until a toothpick inserted in the middle comes out clean about 50-60 minutes.