In the bowl of your stand mixer, fitted with the paddle attachment, place the butter, aquafaba, vanilla and 2 tbsp of sugar.
Slowly start mixing, and once it is more incorporated, turn up the speed to medium for a couple minutes.
Take the lavender and crush it a little in a mortar and pestle.
Add the flour, lemon zest and 1/2 tsp of lavender to the mixer and slowly begin to incorporate the dry ingredients into the wet.
Once the dough is mixed, pull out a large sheet of plastic wrap and lay it on the counter. Pull the ball of dough out of the mixer, and form it into a log. Place the log on the piece of plastic wrap and roll it a little to make it even. Wrap it up tightly, twisting the ends, and then put it into the fridge for at least an hour to rest.
Meanwhile, mix the remaining 1/2 tsp of crushed lavender together with the remaining 2 tbsp of sugar.
Remove the cookie log from the fridge, and unwrap. Slice into 1/2" medallions, and place on a cookie sheet. Sprinkle with the lavender/sugar mixture, then bake in a pre-heated 350 degree oven for about 9-10 minutes.
Remove to a wire rack to cool.