Heat the oven to 325°. Grease a 12-cup muffin pan or line it with muffin cups.
Trim off the ends and grate the zucchini. Wrap up the shredded zucchini in cheesecloth or a flour sack towel (you can try paper towels but they might rip) and wring and squeeze out as much water as possible. When you think you're done, twist and squeeze a bit more.
In a medium bowl, whisk the almond flour, tapioca or arrowroot, coconut flour, cinnamon, baking soda, salt, nutmeg and cream of tartar.
In a large bowl or the bowl of a stand mixer, whisk the coconut sugar, water, eggs, avocado oil, vanilla, lemon zest and juice until blended.
If using a stand mixer with a whisk, with the mixer on low speed, slowly add the dry ingredients then increase the speed to medium until everything is blended. Stop the mixer and scrape down the sides and bottom of the bowl with a spatula. If whisking by hand, whisk in the dry ingredients in 4 or 5 additions.
Give the zucchini one last squeeze and add to the batter along with the chocolate chips. Stir in with a spatula, breaking up the clumps of zucchini, until evenly distributed.
Portion the batter into the muffin pan, filling each cup to to the top. Each cup will probably need 4-6 tablespoons of batter. Sprinkle a few more chocolate chips on top of each one, if desired.
Bake for 30-35 minutes, rotating the pan 180° halfway through, until the muffins are golden brown and a toothpick inserted in the middle comes out clean (unless it pierces a chocolate chip). Let the pan cool on a rack for at least 15 minutes.