Mix the ground flaxseed with 7 Tbsp. of water and set aside to let thicken, about 5-7 minutes.
In the bowl of a stand mixer, add the sugars and lemon zest. Let the mixer run on low for 2-3 minutes to infuse the lemon zest into the sugar. (you can also do this by hand by rubbing the zest into the sugar).
Add the butter to the sugar mixture and let cream together on medium-high until light and fluffy, about 5 minutes.
Add the flaxseed and the vanilla and let cream together an additional 2 minutes.
Sift together the dry ingredients (flour, baking soda, and salt) and add to the mixer all at once. Let the mixer run on low until almost fully incorporated, then add the walnuts and coconut and fold together using a spatula.
Chill the cookie dough for at least 1 hour, overnight if possible.*
When you're ready to bake, preheat the oven to 360ºF (yes, 360! Not 350).
Scoop the cookie dough into balls and place on a parchment-lined baking sheet. Bake for 12-15 minutes (depending on the size of your cookies) until golden brown.
Let the cookies cool completely. When you're ready to ice them, add the powdered sugar and lemon juice to a small bowl. Mix together well until smooth and no lumps remain. Drizzle over the cookies.
*I usually scoop the cookie dough while it's soft, place it on a parchment-lined baking sheet, wrap it in plastic wrap, and chill overnight. It makes it a little easier than trying to scoop cold cookie dough!