Preheat oven to 350ºF. Grease a six-count non-stick doughnut pan with coconut oil or an oil mister.
In a small bowl, mix together the flaxseed meal and water. Set aside.
In a large bowl, mix together the sugar and lemon zest, using your fingers to rub the zest with the sugar to release the oils. Add the flour, baking powder, and salt, stirring together with a whisk until combined.
Drop the coconut oil into the flour mixture. Use a pastry blender or your clean fingers to distribute the coconut oil throughout the mixture until it resembles coarse crumbs.
Add the coconut milk and lemon juice to the small bowl with the flaxseed mixture. Stir.
Make a well in the middle of the dry ingredients and pour in the wet ingredients. Stir with a wooden spoon just until incorporated.
Scoop batter into a large zipper bag and squeeze the contents toward one of the bottom corners. Snip off the corner and use the bag to pipe the dough into each doughnut cup. Divide dough evenly between each cup--I usually go around each cup once or twice, then if I have any batter left over, I go back and add to each cup. You can also use a pastry bag affixed with a plain round tip.
Bake for 8-10 minutes, or until doughnuts are puffed and spring back when gently poked.
Allow the doughnuts to cool in the pan for five minutes, then use a butter knife to gently loosen the edges. Invert the doughnuts onto a baking rack set over a rimmed baking sheet and let cool completely.
To make the glaze, place the powdered sugar, lemon zest, and coconut milk into a small bowl and beat with a fork until it forms a liquid about the consistency of molasses. Dip each doughnut in the glaze and set glaze-side-up back on the baking rack. Sprinkle doughnuts with coconut.
Doughnuts keep at room temperature in an airtight container for up to 3 days.