Preheat the oven to 350. Grease a 12-cup muffin pan.
In a medium bowl, whisk together eggs, coconutmilk and vanilla. Set aside.
In a bowl of an electric mixer (or in a separate bowl using hand mixer)…sift the flour baking powder and baking soda. Add the sugar and salt. Mix the dry ingredients on low for about 30 seconds (until well combined).
Add the butter and half of the egg mixture. Mix on low until just combined. Scrape the sides and bottom. Change the speed to medium and beat for about a minute. The batter will start get light and airy.
Add the other half of the egg mixture slowly, in two batches, beating for about 30 seconds after each addition. While it's beating, pour in the lemon juice and add the lemon zest. The cake batter will be light and fluffy at that point.
Divide the batter among the muffin cups and bake for 18-20 minutes. Do a toothpick test at 18 minutes to see if it's done.
To prepare the glaze, mix powder sugar and lemon zest together. Heat up the coconutmilk and stir it into the sugar mixture. Stir until smooth.
Pour some of the glaze over the muffins and sprinkle with coconut flakes.