Preheat the oven to 350° F. Butter an 8-inch diameter, 2 1/2-inch deep cake pan and line the bottom with parchment paper.
Put the granulated sugar and lavender into a food processor and whizz until the lavender has broken down. Sift the flour, baking powder, baking soda, and salt together into a bowl. Stir in the lavender sugar. In a pitcher, mix the eggs with the yogurt and oil. Make a well in the center of the dry ingredients and gradually stir in the wet ingredients. Add the lemon zest and juice, but don’t over-mix. Scrape the batter into the prepared pan.
Bake for 45 to 50 minutes, or until the cake is coming away from the inside of the pan and a skewer inserted into the middle comes out clean. Turn it out, peel off the paper, and set on a wire rack until cold. Dust with confectioners’ sugar just before serving and decorate with sprigs of fresh lavender.