1) To make the cupcakes: Preheat the oven to 375°F. Place cupcake liners in the 12 cups of a muffin pan. Position an oven rack in the middle of the oven.
2) Beat together the oil, sugar, lemon juice powder, salt, and lime zest until light in color, about 2 minutes at medium-high speed.
3) Beat in the lime juice; then the eggs, one at a time, until the mixture lightens in color, about 2 minutes at medium-high speed.
4) In a separate bowl, whisk together the flour and baking powder.
5) At low speed, add the flour mixture to the batter in three additions, alternating with two additions of the milk; mix until blended, about 30 seconds.
6) Scoop the batter into the prepared muffin pan, filling each cup about 2/3 full.
7) Bake until a cake tester inserted into the center of a cupcake comes out clean, 16 to 20 minutes; the cakes will remain quite pale.
8) Remove from the oven, and after 5 minutes transfer to a rack to cool.
9) To make the glaze: Whisk together the ingredients to make a smooth glaze about the consistency of molasses, adding additional liquid or confectioners' sugar as needed.
10) To glaze cupcakes: Dip cooled cupcakes into the glaze. Sprinkle with zest, if desired; the glaze sets up quickly, so be sure to sprinkle with zest right after dipping.
Yield: 12 cupcakes.