Sift flour, 1/3 cup sugar, and baking powder together in a bowl. Cut cold butter into flour mixture using a pastry cutter or two forks until mixture is crumbly.
Mix yogurt mixture, 2 tablespoons melted butter, egg, lavender, and lemon zest in a separate bowl. Stir yogurt-lavender mixture into flour mixture until just moistened.
Turn dough onto a lightly floured surface and gently knead 8 to 10 times, adding more flour if dough is too sticky.
Divide dough into 2 pieces and place on an ungreased baking sheet. Pat and shape each piece into a 6-inch circle. Score each circle into 6 wedges using a sharp floured knife. Brush tops with 1 tablespoon melted butter; sprinkle with 1 teaspoon white sugar.
Bake in the preheated oven until scones are just golden, 10 to 12 minutes. Remove from oven, break into wedges, and cool on a wire rack.