Preheat oven to 400°F (204°C). Line a baking sheet with parchment paper.
In a large bowl, whisk together the flour and baking powder. Set aside.
In a blender, food processor, or mortar and pestle, combine sugar, lavender, lemon zest, and vanilla extract. Blend or grind until fragrant and well combined. Set aside.
In a small bowl, whisk together the egg and yogurt until smooth.
Grate the frozen butter into the flour mixture. Using a pastry cutter or your fingers, work the butter into the flour until the mixture resembles coarse crumbs with pea-sized pieces of butter throughout.
Make a well in the center of the dry ingredients. Pour in the egg-yogurt mixture and add the lavender lemon sugar. Gently mix until a thick dough forms. Do not overwork.
Transfer the dough onto the prepared baking sheet and gently pat into an 8-inch circle. Using a sharp knife, cut the dough into 8 wedges. Brush the tops with 2 tablespoons buttermilk. Separate the wedges slightly on the baking sheet, leaving space for them to expand while baking.
Bake for 20 minutes, or until golden brown and set. Transfer to a wire rack and let cool.
Icing: Add the powdered sugar, lemon juice, and vanilla extract to a small bowl and stir until combined. Drizzle over scones after scones have cooled for a few minutes.