Using the paddle attachment of a stand mixer, or using an electric hand mixer, cream together vegan butter and granulated sugar until light and fluffy (2-3 minutes), stopping once to scrape down the bowl.
Add in the ground flax seed, lemon juice, lemon zest, and vanilla extract, and mix until well combined.
Next, remove mixing bowl from the stand mixer and add the flour, baking soda, and salt. Use a rubber spatula or wooden spoon to mix by hand, mixing just until combined. Do not overmix or you will end up with tough cookies.
Cover bowl with plastic wrap and chill in the refrigerator for at least 30 minutes.
Preheat the oven to 350 degrees F. Line two baking sheets with parchment paper, and place 2 tablespoons of granulated sugar into a small bowl.
Using a small cookie scoop, place 1 tablespoon-sized scoops of cookie dough onto baking sheet. Then, using the palms of your hands, roll cookie dough into balls, roll in the bowl of sugar to coat each ball, and return to cookie sheet. There should be 12 cookies per baking sheet.
Bake for 12-14 minutes, until the bottoms are lightly golden and the cookies are cooked through but still slightly soft. The cookies will continue baking after they're removed from the oven, so don't worry about under-baking them.
After removing cookies from the oven, give the baking sheets a few taps on the counter to help create the perfect crinkly texture. Let the cookies cool for 7-10 minutes, then transfer to a wire rack to cool completely.