Make the cake: Heat oven to 350 degrees. Line a 9-by-13-inch baking pan with parchment paper, butter and flour the paper.

In a measuring cup with a spout, combine the milk and lemon juice. Whisk the flour, baking powder, baking soda and salt together in a medium bowl.

In the bowl of a stand mixer fitted with the paddle attachment, cream butter, sugar and lemon zest until light and fluffy, about 5 minutes. Add eggs, one at a time, mixing for about 30 seconds after each. Scrape down bottom and sides of the mixer to ensure the mixture is well combined. With the mixer on low speed, alternately add the flour mixture and milk mixture to the bowl in three additions. Mix until just combined, then use a rubber spatula to finish mixing the batter.

Pour the batter into the prepared pan, smooth the top and tap the pan on the counter a few times to release any large air pockets. Bake for 35 to 40 minutes or until puffed and golden and a cake tester inserted into the center comes out clean. Cool the cake completely on a rack before frosting.

Meanwhile, prepare the frosting: Combine the butter, confectioners' sugar, lemon zest and a pinch of salt in the bowl of a stand mixer fitted with the paddle attachment. Mix on low until combined, then turn the mixer up to medium-high and stream in 3 tablespoons of lemon juice. Whip the frosting until very light and fluffy, about 5 minutes, adding additional lemon juice as necessary until frosting is smooth and spreadable.

Spread the frosting over the cooled cake and serve. Store leftover cake at room temperature, covered for up to 2 days.