Preheat an oven to 350 degrees F (175 degrees C). Grease and flour 3 8-inch cake pans.
Mix the cake mix, water, eggs, and vegetable oil as directed on the package, and pour batter into prepared cake pans.
Bake the layers in the preheated oven until a toothpick inserted into the center of a cake comes out clean, 30 to 35 minutes. Let cool in pan at least 20 minutes or until completely cool.
When the cake is completely cool, run a paring knife between the cake and the edge of the pan. Hold the cake pan on its side and gently tap the sides of the pan against the counter to loosen it. Cover the cake pan with a plate or cooling rack, and invert it to tip the cake out of the pan and onto the plate.
To fill and decorate, lay a cake layer onto an oven-safe plate, and spread half the lemon filling over the bottom layer. Place a second layer gently on the lemon filling, and spread the rest of the filling on the top of the second layer. Top with third layer.
Beat the egg whites in a bowl until they form stiff peaks, then gradually add the sugar and continue to beat until the mixture forms a fluffy, shiny meringue. Spread the meringue all over the cake like a frosting, spreading it into decorative peaks and swirls. Place the decorated cake back into the hot oven, and bake until the peaks and swirls of meringue are lightly browned, about 10 minutes. Refrigerate 4 hours to overnight, then serve cold.
