Cook the lasagna noodles according to the package directions, being sure to add a teaspoon of oil to the cooking water. Rinse and drain.
In a nonstick skillet, brown the meat and drain off any excess fat. Heat the sauce and add the meat to the sauce along with the sugar.
Combine the cottage cheese, eggs, and cayenne.
Preheat the oven to 350 degrees F. To assemble the lasagna, spoon a thin layer of sauce on the bottom of a 9-inch by 13-inch pan. Place a layer of noodles, another thin layer of sauce, a layer of the cottage cheese mixture, then the mozzarella. Repeat until the pan is filled. End with a final layer of sauce and Parmesan cheese. Gently pour milk over the top. Cover with foil and bake for 1 hour. Uncover and let stand for 5 to 10 minutes before cutting into serving-size pieces.
Highly recommended! The prepared sauce makes it quicker and easier to fix than most lasagna recipes, and the results are better, our tester reports, than many restaurant versions. A good do-ahead dinner, too.