Preheat your oven to 350 degrees, line a cookie sheet with a Silpat, grease it or parchment paper, and set it aside.
Take a small cup and make your flax egg, let sit a few minutes to gel.
Get your stand mixer and add your sugar and soft vegan butter; whip until light a fluffy.
Add your wet ingredients; vanilla extract, lemon juice, and flax egg, and stir to combine. Then add your lemon zest and baking powder until evenly combined. Now add your last dry ingredient; your flour, and stir until combined.
These are most like drop cookies, so take your cookie scoop and drop them as evenly as you can on your prepared cookie sheet.
Bake in the preheated oven for 7-8 minutes do not overbake.
Let cool on a cooling rack.
While cooling, make the icing. Take a small bowl and combine the powdered sugar and lemon juice; use a whisk or fork to mix until smooth. Drizzle the lemon icing over the cooled cookies.