Cook noodles according to package directions, omitting salt and fat. Drain and set aside.
Coat a large nonstick skillet with cooking spray; place over medium-high heat until hot. Add mushrooms, carrot, and onion; saute 5 minutes.
Remove vegetable mixture from heat, and stir in tomato sauce, tomato paste, olives, oregano, basil, and pepper. Set mixture aside.
Drain spinach, and press between paper towels to remove excess moisture. Combine spinach, cottage cheese, nonfat cream cheese, and lemon juice. Set spinach mixture aside.
Place 3 lasagna noodles in bottom of an 11- x 7- x 1 1/2-inch baking dish coated with vegetable cooking spray. Spoon one-third of spinach mixture over noodles. Spoon one-third of vegetable mixture over spinach mixture. Top with one-third of mozzarella cheese. Repeat layers twice with remaining noodles, spinach mixture, vegetable mixture, and mozzarella cheese. Top with Parmesan cheese. Bake, uncovered, at 325° for 30 to 35 minutes or until thoroughly heated. Let stand 10 minutes before serving.
If desired, cover and chill overnight before baking. Bake, uncovered.