Place a rack in the center of the oven and preheat the oven to 350 degrees F. Set aside an ungreased 9- by 13-inch pan.

For the crust, place the cake mix, melted butter, and egg in a large mixing bowl. Blend with an electric mixer on low speed for two minutes. Stop the machine and scrape down the sides of the bowl with a rubber spatula. The batter should come together in a ball. With your fingertips, pat the batter evenly over the bottom of the pan, smoothing it out with your fingers until the top is smooth. Set the pan aside.

For the filling, rinse and dry the lemons well. Grate the zest from the lemons and set aside; you should have about 2 teaspoons. Cut the lemons in half, and squeeze into a small bowl; you should have about 6 tablespoons. Set the juice aside.

Place the cream cheese in the same mixing bowl that was used to make the crust, and with the same beaters (no need to clean either) blend with an electric mixer on low speed until fluffy, 30 seconds. Stop the machine and add the lemon juice, lemon zest, eggs, melted butter, and cornmeal and beat on medium speed for 1 minute. Stop the machine and add the confectioners' sugar. Beat on medium speed until the sugar is well incorporated, 1 minute more. Stop the machine and scrape down the sides of the bowl with the rubber spatula so that the filling covers the entire surface and reaches the sides of the pan. Place the pan in the oven.

Bake the cake until it is well browned but the center still jiggles when you shake the pan, 45 to 47 minutes. Remove the pan from the oven and place it on a wire rack to cool, 30 minutes. Cut into squares and serve.

Store this cake, covered in aluminum foil, at room temperature for up to 4 days, or in the refrigerator for up to 1 week. Or freeze it, wrapped in foil, for up to 6months. Thaw the cake overnight in the refrigerator before serving.