Preheat oven to 400 degrees F (200 degrees C). Line a rimmed baking sheet with parchment paper.
Combine 3/4 cup plus 2 tablespoons sugar, 1/4 cup butter, and 2 teaspoons vanilla sugar in a large bowl; beat with an electric mixer until smooth and creamy. Add eggs one at a time, beating well after each addition. Beat in lemon zest with the last egg.
Combine 2 3/4 cups flour and baking powder. Sift over butter mixture and quickly beat into batter with the electric mixer running on low speed.
Combine apple slices, lemon juice, and cinnamon sugar in a bowl and fold into batter. Spread batter onto the prepared baking sheet. Spoon applesauce onto batter and spread out evenly.
Combine 1 cup plus 2 tablespoons flour, 1/2 cup cubed butter, 1/2 cup plus 2 tablespoons sugar, almond meal, and 2 teaspoons vanilla sugar in a bowl and mix into streusel. Sprinkle streusel over applesauce.
Bake in the preheated oven until streusel is lightly browned and cake is set, about 40 minutes.