Have all the ingredients at room temperature.
Position a rack in the lower third of an oven and preheat to 325°F. Grease a cake pan; tap out excess flour.
To make the cake, over a sheet of waxed paper, sift together the flour, baking powder, baking soda and salt; set aside.
In the bowl of an electric mixer fitted with the flat beater, beat the butter on medium speed until creamy and smooth, about 30 seconds. Add the granulated sugar and lavender and continue beating until light and fluffy, about 5 minutes, stopping the mixer occasionally to scrape down the sides of the bowl. Add the eggs a little at a time, beating well after each addition, then beat in the lemon extract.
Reduce the speed to low and add the flour mixture in three additions, alternating with the yogurt and beginning and ending with the flour. Beat each addition until just incorporated, stopping the mixer occasionally to scrape down the sides of the bowl. Using a rubber spatula, fold in the lemon zest.
Spoon the batter into the prepared pan, spreading the batter so the sides are higher than the center. Bake until the cake begins to pull away from the sides of the pan and a toothpick inserted into the center of the cake comes out clean, about 1 hour. Transfer the pan to a wire rack and let the cake cool upright in the pan for 15 minutes.
To make the glaze, in a bowl, whisk together the confectioners’ sugar, lemon juice and milk. Spoon the glaze over the cooled cakelets and serve.