Preheat oven to 375 degrees F (190 degrees C). Grease 3 9-inch cake pans.
Beat whites of 4 eggs in a glass or metal bowl until foamy. Continue to beat until stiff peaks form. Lift your beater or whisk straight up: the tip of the peak formed by the egg whites should curl over slightly. Set aside. Reserve egg yolks in a small bowl. Sift together cake flour and baking powder in a separate bowl.
Beat 3/4 cup butter, 2 cups sugar, and 1/2 teaspoon salt with an electric mixer in a large bowl until light and fluffy. The mixture should be noticeably lighter in color. Add reserved egg yolks one at a time, allowing each yolk to blend into the butter mixture before adding the next. Pour in cake flour mixture alternately with 1 cup milk, mixing until just incorporated. Stir lemon juice and 1 teaspoon vanilla extract into batter.
Whisk beaten egg whites a few times; use a whisk or rubber spatula to fold 1/3 of the egg white mixture into the batter to lighten it. Fold in remaining egg whites, mixing just until combined. Pour batter into prepared pans and spread evenly over bottom.
Bake in preheated oven until cake is light golden brown and just pulling from the sides of the pan, 15 to 20 minutes. Do not overbake. Cool in pans for 5 minutes, then invert onto cooling racks to cool completely.
To make custard: combine 1 1/2 cups sugar, 1/2 teaspoon salt, 1/4 cup flour, cornstarch, and 1/4 cup cocoa powder in a saucepan and mix well. In a separate bowl, whisk remaining 1/2 cup sugar into 4 beaten eggs. Pour 4 cups whole milk into saucepan and cook over medium heat, stirring constantly, until mixture begins to boil. Remove from heat and gradually pour hot milk mixture into egg mixture, whisking constantly. Add chopped chocolate and stir until chocolate melts.