Position a rack in the center of the oven and preheat to 350 F. Lightly spray an 8-inch square baking pan with oil. In a medium bowl, whisk the flour, Rumford Baking Powder and salt until well combined. Set aside. In another medium bowl, using a handheld electric mixer set at high speed, beat the applesauce, sugar, egg, egg whites, oil, lemon zest and vanilla until frothy, about 2 minutes. Make a well in the center of the dry ingredients and pour in the applesauce mixture. Using a spoon, stir just until combined. Do not overmix. Using a gentle touch, spread the batter into the prepared pan.
Bake until the top of the cake springs back when pressed gently in the center and the edges are lightly browned, 30 to 35 minutes. Do not overbake. Cool in the pan on a wire cake rack for 15 minutes. Unmold onto the rack, turn right side up, and cool completely.
Lemon Glaze: Place the powdered's sugar and zest in a medium bowl.
Stir in enough of the lemon juice to make a smooth glaze. The consistency should be a little thicker than heavy cream. When cake is cool, glaze it with the lemon glaze, letting it drip down the sides. Let stand until the glaze sets.