Position a rack in the upper third of the oven and preheat the oven to 350°F. Lightly oil the cups of a muffin pan or line it with paper liners.
Mix the almond or soy milk and apple cider vinegar together and set aside.
In a large bowl, whisk together the flour, poppy seeds, baking soda, baking powder, and salt.
In a medium bowl, whisk together the lemon juice, lemon zest, sugar, coconut oil, vanilla, and almond or soy milk mixture.
Pour the wet mixture into dry mixture and mix until there are no visible lumps of flour. Do not overmix. The batter will be thick.
Carefully fold in the zucchini.
Divide the batter among the muffin cups, filling them ¾ of the way full.
Bake until the muffins are golden brown around the edges and toothpick inserted in the center comes out clean, about 17 to 20 minutes.
Place the muffin tin on a wire rack and allow the muffins to cool for 10 minutes before carefully removing them.