Preheat the oven to 350 degrees F (175 degrees C). Bring a large pot of lightly salted water to a boil. Add lasagna noodles, and cook until tender, about 8 minutes. Drain, and rinse noodles, and set aside.
In a medium bowl, mix together the Cheddar cheese, ricotta cheese, egg, white sugar, and almond extract. Spread one can of apple pie filling in the bottom of a 9x13 inch baking dish. Layer half of the noodles to cover the filling. Spread the cheese mixture over the noodles. Top with the remaining noodles, and spread the remaining can of apple pie filling over the top of those.
In a small bowl, stir together the flour, 6 tablespoons brown sugar, oats, cinnamon and nutmeg. Mix in margarine until the mixture is crumbly. Sprinkle over the top of the pie filling.
Bake for 45 minutes in the preheated oven. Cool for 15 minutes. While the lasagna cools, stir together the sour cream and 1/3 cup brown sugar. To serve, cut into squares and top with sour cream as a garnish.