Preheat oven to 350°F. Spray a 9x13” pan with nonstick cooking spray (the kind with flour) or grease the pan with butter or shortening and flour.
Stir the flour, baking soda, baking powder, and salt in a large bowl. Set aside.
Cream butter and granulated sugar in a large bowl with a hand mixer or a stand mixer fitted with the paddle attachment. Cream until light and fluffy, about 2-3 minutes.
Add the milk, lemon juice, zest, and eggs to a large measuring cup or bowl. Whisk until combined.
Add the wet and dry ingredients into the creamed butter in two additions, mixing between each, just until the mixture is combined. Don't over mix!
Pour batter into prepared pan. Bake 25-43 minutes, until a toothpick comes out clean. Cool completely before frosting.
To make the frosting: cream butter and powdered sugar until crumbly. Add salt, lemon juice and 1 tablespoon milk. Mix until smooth, adding more milk 1 teaspoon at a time until you've reached desired spreading consistency.
Frost cooled cake and serve.