Prepare pasta according to package information, drain and set aside.
In a large skillet, brown Italian sausage until fully cooked and no longer pink. Set aside.
In a bowl, combine eggs, garlic, 1 ½ cups mozzarella cheese, ½ cup Parmesan cheese, yogurt, oregano, and salt. Stir until combined.
Combine pasta sauce with finely shredded zucchini and carrot.
Preheat oven to 350°F. Spray a 9 x 13 inch baking pan with nonstick spray. Spoon ⅓ cup of pasta sauce over the bottom of the baking pan. Top sauce with ⅓ of the spaghetti, followed by half of the cheese mixture, half of the meat mixture and another ⅓ of the sauce. Repeat layers ending with the remaining pasta sauce. Top lasagna with 1 cup of mozzarella and ½ cup Parmesan cheese.
Cover lasagna with foil and bake for 30 minutes. Remove foil and bake an additional 20 minutes.