Mix your ground flax seed and water in a small bowl. Let sit in the fridge while you prepare the dry mixture. It will firm up while cooling, about 5 minutes. This will act as your egg substitute.

In a medium bowl, combine flour, baking powder, and salt. Set aside.

In a large bowl, add flax egg, softened butter, sugar, vanilla, lemon zest, and lemon juice. If you have a stand mixer or hand mixer, I recommend creaming these ingredients together. This will incorporate some air into the mixture that provides lift to the cookies. If you do not have a mixer this is OK, just whip the ingredients swiftly with a fork until a soft mass is formed. Remember, you want you butter to be soft but not melted.

Preheat the oven to 350 degrees F. Add dry mixture to wet, gently combining with a wooden spoon until no dry spots remain. Line two baking sheets with parchment paper or a nonstick mat. Add granulated sugar and powdered sugar to two separate bowls.

Using a TBS measure or spoon, form balls of dough. Roll each ball in granulated sugar and then powdered sugar. Place cookies on prepared sheet, pressing down slightly. Pressing the balls down also helps them bake more evenly and prevents awkward spreading.

Bake for 8-10 minutes. They will look underdone when you remove them from the oven, which is good. Let them continue baking on the sheets once outside the oven; they'll firm up as they cook and stay softer. Store in a covered contained for 5 days.