In a medium mixing bowl, combine the flour, arrowroot starch, baking soda, and salt. Set to the side.
In a stand mixer (with paddle attachment) or using an electric handheld mixer, cream together the butter and sugar until fully combined and creamy. It should take about 1 - 2 minutes.
Next, add the lemon juice, almond milk, and vanilla. Mix until combined, be careful not to overwhip.
Add the flour mixture in two parts and mix until the dough is combined and slightly “sticky.” Add in the lemon zest when you add the second portion of flour.
Next, cover your mixing bowl with plastic wrap and place it in the fridge to let the dough chill for 45 minutes to 1 hour. You can let it chill for up to 2 - 6 hours if needed.
When your dough is almost done chilling, preheat your oven to 350°F and line two rimmed cookie sheets with parchment paper. Add rolling sugar to a small bowl.
When the cookie dough is ready, use a cookie scooper to portion out about 1.5 Tablespoons of dough for each cookie. Use your hands to roll them into balls, then gently roll each dough ball in the sugar topping. Evenly space them out on your lined cookie sheets. This recipe makes about 22 - 26 cookies.
Bake for 10 - 12 minutes. They will look puffed up, pale, and underdone - that is ok! They will continue to bake as they cool. Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack. Enjoy!