To make the cakes, preheat the oven to 350°F. Grease two baking sheets, or line them with parchment.
In a large bowl, whisk together the flour, baking soda, baking powder, and sea salt.
In the bowl of a stand mixer, beat together the butter, granulated sugar, brown sugar, and oil. Beat in the eggs.
Add the dry ingredients and the milk alternatively to the butter mixture in three additions, beginning and ending with the dry ingredients. Beat well.
Stir in the shredded zucchini and lemon zest.
Using a 2-ounce scoop, place six mounds of batter on each cookie sheet, leaving 2 inches between mounds. This will use half the batter.
Bake the cakes for 15 to 20 minutes, rotating the pans once. The cakes are done when they are dry and spring back when you press them lightly with your finger.
Remove them from the oven, transfer to a cooling rack, and then repeat steps 6 and 7 with the remaining batter.