Cook lasagna noodles following packaged directions. In a colander, drain and run under cold water until cool to the touch.
Complete steps 3-9 while noodles cook. (Optional to skip this step and add uncooked pasta in Step 10).
Rinse greens, mushrooms, and zucchini. Peel garlic.
Grate mozzarella cheese. Set aside 1/4 cup grated cheese for topping lasagna.
In a medium bowl, add spinach, mushrooms, and zucchini. Stir in 1/4 tsp of the salt. Set over a colander to drain. When completely drained, pat veggies dry with paper towels.
Stir garlic, basil, oregano, remaining 1/4 tsp salt and black pepper into canned tomatoes to make the sauce. Mix in can.
In a medium bowl, crack egg and beat with a fork. Add cheeses and mix.
Lightly coat a 9-by-13 inch baking dish with non-stick cooking spray. Spread 1/2 cup tomato sauce in bottom of the dish.
Layer 3 noodles over sauce. Then layer 1 cup cheese mixture, 1.5 cups veggies, and 2/3 cup tomato sauce. Repeat layers 2 more times, ending with noodles. Cover with remaining sauce and reserved cheese.
Bake until cheese is melted and lightly browned on top and lasagna is bubbly, about 45 minutes. Remove from oven. Let cool 10 minutes before cutting.