Heat the oven to 375 degrees F. Butter an 8-inch square pan or equivalent-size baking dish. I buttered my pan with melted butter.
Mix together the flour, baking powder, and salt in a small bowl. Cream together the butter and 1 cup of the sugar. Stir in the eggs and vanilla in with the butter and sugar mixture. Add the flour mixture and beat until combined. Spread the mixture evenly in the prepared pan.
n a small bowl, combine the remaining 1/3-cup sugar with the cinnamon. Pour the lemon juice into a medium bowl. Core and slice the apples into the bowl. I left the peels on my apples. Add the cinnamon-sugar mixture and stir to coat thoroughly. Arrange the apple slices on top of the batter in overlapping rows, pressing lightly into the batter. Bake for 45 minutes until the cake is golden brown. Cool for 10 to 15 minutes before serving. Serve with vanilla ice cream for a great treat after a large meal!