Preheat oven to 350 degrees F. Butter an 8-inch square cake pan.
Add sliced apples to prepared cake pan. In a small bowl, combine lemon juice, 1/2 cup sugar, and water; pour over apples and mix thoroughly. Let stand while preparing batter for cake.
In a large bowl, combine flour, remaining 3/4 cup sugar, baking powder, and salt; cut in butter or vegetable shortening with a pastry blender until shortening is the size of very small peas. Make a hollow in the center of the flour mixture, and add egg and milk; mix until just combined (batter should have small lumps in it).
Pour batter over apple mixture and bake approximately 45 minutes or until a toothpick inserted near the center comes out clean.
Prepare Lemon Sauce. Serve with Lemon Sauce spooned over warm cake.
In a small saucepan, mix sugar and cornstarch thoroughly. Stir in cold water until cornstarch is dissolved. Add boiling water and cook over medium heat, stirring constantly until thickened and clear in color.
Remove from heat and stir in butter, lemon extract, and lemon juice; set aside until ready to serve.
Apple Cake with Lemon Sauce Recipe: https://whatscookingamerica.net/cake/applecake.htm