Pre-heat oven to 375 degrees F. Prepare two cookie sheets with parchment paper.
Sift flour and baking soda into a large mixing bowl. Set aside.
In a separate mixing bowl, cream butter and sugar with a hand mixer. Scrape the sides of the bowl with a silicone spatula.
Once the sugar and butter look creamy, pour in the flax egg mixture, lemon juice, and vanilla extract.
Use a small-medium cookie scoop to keep the cookie size consistent. Scoop on the parchment paper and leave a two-finger gap in between.
Bake for 15 minutes or until the cookies are golden. Remove from the oven. Wait 5 minutes and brush them with the lemon icing while they are still hot.