These are not only gluten free, but dairy free too! They can be a bit fragile during baking so they need to be chilled before putting in the oven to bake. Because of the difference in weights between flour blends I have used volume measurements instead of weight for this recipe. Lavender can be found at Bulk Barn if you are in Canada.

Ingredients
Cookies
2/3 cup sugar
2 tsp lemon zest
1/2 tsp dried culinary lavender
3/4 cup unsalted margarine, at room temperature
1 tsp vanilla extract
1/8 tsp salt
1 3/4 cups gluten free flour blend
1 1/2 Tbsp sugar (for sprinkling)
Glaze
1 cup powdered sugar (sifted)
1 tsp lemon zest
2 Tbsp lemon juice
1 tsp dried culinary lavender for sprinkling
Directions
Combine sugar, lemon zest, and lavender in a food processor and pulse for 1 minute until lavender is finely chopped. Beat margarine and sugar mixture in a large bowl with a hand mixer at medium speed (or a stand mixer with the paddle attachment) until combined; add vanilla and salt and beat until incorporated. Scrape down bowl as needed. Reduce speed to low and mix in flour just until incorporated and dough begins to come together in large pieces.
Scrape dough out onto a piece of plastic wrap, shape into a disk and wrap well. Chill dough in the refrigerator until firm, about 30 minutes.
Adjust oven rack to upper-middle and lower-middle positions and preheat oven to 350°F. Line two baking trays with parchment paper. Lightly flour your work surface and your rolling pin and roll out dough to slightly less than 1/4-inch. Using a floured 2 1/2-inch fluted biscuit cutter cut out the cookies and place on the baking sheet about 1 inch apart. You may want to use a small spatula or bench scraper to move the coolies to the baking sheets. You can combine any scraps and roll them out again and continue to cut out cookies until you have 24.
Take both baking sheets and place in the refrigerator for at least 2 minutes to chill and firm before baking, this will help the cookies keep their shape and not spread.
Bake for 14 to 15 minutes rotating the cookie sheets top to bottom and back to front halfway through for even baking. Bake until lightly golden and edges are set. Cool for 5 minutes on baking sheets, then transfer to a wire rack to cool completely before glazing.
For the glaze, whisk together powdered sugar, lemon zest, and juice in a small bowl. Transfer glaze to a small piping bag and drizzle over cookies and sprinkle with lavender buds; let set before serving.