Combine spinach, cottage cheese, and egg substitute in a medium bowl; stir well, and set aside.
Heat oil in a large saucepan over medium-high heat. Add onion; sauté 3 minutes or until tender. Add mushrooms and garlic; sauté 2 minutes or until mushrooms are tender. Add tomatoes and next 7 ingredients; stir well. Reduce heat, and simmer, uncovered, 20 minutes. Remove tomato mixture from heat; set aside.
Coat a 13 x 9-inch baking dish with cooking spray. Spoon one-third of tomato mixture into baking dish. Arrange 3 uncooked noodles lengthwise in a single layer over tomato mixture; top with 1 1/4 cups spinach mixture. Layer 2 1/2 cups zucchini over spinach; sprinkle with 1/2 cup mozzarella cheese. Repeat layers; top with remaining tomato mixture. Cover and chill 8 hours.
Preheat oven to 350°.
Remove lasagna from refrigerator; bake, covered, at 350° for 1 hour and 30 minutes. Uncover; sprinkle with 1/2 cup mozzarella cheese and Parmesan cheese. Cover; let stand 5 minutes before serving.