Preheat the oven to 350°F (175°C).
In a large nonstick skillet over medium-high heat, cook the ground beef or turkey, stirring and breaking it up, until browned; drain any excess fat.
Add the marinara sauce to the browned meat, bring to a boil, then reduce heat and simmer for 5 minutes.
While the meat simmers, combine the fat-free cottage cheese and grated Parmesan in a bowl and stir until smooth.
Lightly coat a 13x9 inch baking dish with cooking spray. Spread 1/2 cup of the meat-and-sauce mixture in the bottom of the dish.
Arrange 4 no-boil lasagna noodles over the meat layer. Top with half of the cottage cheese mixture, 1 cup of the meat mixture, and 1/3 cup of the shredded cheddar.
Repeat the layers: 4 noodles, remaining cottage cheese mixture, 1 cup meat mixture, and 1/3 cup cheddar. Finish with a final layer of noodles and spread the remaining meat mixture over the top.
Cover the dish and bake for 30 to 35 minutes, until the noodles are tender.
Uncover, sprinkle the remaining 1/3 cup shredded cheddar (or mozzarella) over the top, and bake an additional 5 minutes until the cheese melts.
Let the lasagna stand for 10 minutes before cutting into 9 servings. Garnish with chopped parsley if desired.