Preheat oven to 350F. Grease and line a 8x8-inch baking pan. (See below in “NOTES” section for other baking pan alternatives).
In a medium bowl, whisk together the flour, baking powder and salt. Set aside.
In the bowl of a stand-up mixer with the paddle attachment (alternatively you can do this in a large bowl with an electric mixer), add the sugar and lemon zest. Beat the two together. This will release all of the fragrant oils in the lemon zest and infuse them in the sugar. We want this, we need this.
Add the butter and vanilla extract; beat until light and fluffy, about 2 to 3 minutes. If you want the cake to be yellow in color, add 2-3 drops of food coloring gel. This is of course optional.
In a measuring cup, pour in the milk, egg whites, and add the strained lemon juice.
Turn the mixer to low speed and, alternating between the dry ingredients and the liquid ingredients, add them to the butter/sugar mixture, until the batter is relatively smooth.
Pour the batter into the prepared baking pan and smooth it out until it reaches the sides. Transfer to the oven to bake for 25 to 32 minutes, until a skewer inserted into the center comes out clean.
Allow the cake to cool in the pan for about 10 minutes and then invert onto a cooling rack and cool to room temperature. It’ll probably take a good hour.