Preheat the oven to 350F.
In a small bowl or measuring cup, stir the lemon juice into the milk and let it sit while you mix the rest of the batter.
In a large bowl, whisk together the flour, sugar, cocoa, baking powder, baking soda and salt. In another bowl, whisk together the oil, mayonnaise, applesauce and vanilla. Add to the dry ingredients along with the milk, and stir just until combined. Add the hot coffee, and whisk until the batter is smooth.
Spray two 8 or 9-inch round or square cake pans or a 9x13-inch pan with nonstick spray and divide the batter between them (or pour into a 9x13-inch pan). Bake for 25-30 minutes or until slightly domed and the middle of the cakes are springy to the touch. Cool completely before frosting.
To make the frosting, beat the frosting, icing sugar, cocoa, 2 Tbsp milk or water and vanilla until smooth and lighter in texture, adding more liquid or sugar as needed to make a spreadable frosting. (If you use unsalted margarine, add a pinch of salt.) Spoon into a piping bag with a star tip and pipe rows of frosting blossoms on top of the cake, or spread it over the top with a knife. Makes 2 smaller single-layer cakes or one 9x13-inch sheet cake.