Make the lemon filling:
Combine the sugar, cornstarch, and salt in a medium nonreactive saucepan. Gradually stir in the water and bring to a boil, stirring constantly, over medium heat. Cook, stirring, for 1 minute. Remove from the heat and stir in the butter and lemon zest. Gradually whisk in the lemon juice. Let cool completely before using.
Make the berry topping:
Put the berries in a bowl and sprinkle with the sugar. Toss gently and let stand for 1 hour or so while you prepare the cake.
Make the cake:
Preheat the oven to 350 degrees F. Grease and flour two 8-inch round cake pans. In a large mixing bowl, blend the flour, sugar, baking powder, and salt. With an electric mixer on medium speed, beat in the shortening, 2/3 cup of the milk, and the vanilla. Beat for 2 minutes, frequently scraping down the sides of the bowl. Add the remaining 1/3 cup of milk and the egg whites, and beat for 2 minutes more, scraping down the sides of the bowl.
Pour the batter into the prepared pans and bake until the center of each cake springs back when lightly touched, 30 to 35 minutes. Remove from the oven and let cool in the pans for 10 minutes. Remove the cakes from the pans and let cool completely on wire racks.
Make the frosting:
Beat the egg whites in a large bowl with an electric mixer until they hold a soft peak. Meanwhile, mix the sugar, corn syrup, and water in a large saucepan and bring to a rolling boil. Cook to 242 degrees F on a candy thermometer, or until a tiny bit of syrup dropped into a bowl of cool water and then pulled between the thumb and forefinger spins a 6- to 8-inch thread. With the mixer running, pour the hot syrup very slowly into the beaten egg whites. Continue beating with the electric mixer until the frosting holds stiff peaks. Beat in the vanilla and use immediately.
Place one of the cake layers upside down on a cake platter and, with a flexible spatula, spread the lemon filling almost to the outer edge. Place the second layer right-side up on the filling. Frost the sides, bringing the frosting up to form a rim around the edge of the top layer. Spread the frosting evenly over the top, making attractive s