Heat a large Dutch oven coated with cooking spray over medium-high heat. Add onion; sauté 4 minutes or until tender. Add spinach; sauté 1 1/2 minutes or until spinach wilts. Combine provolone, parsley, salt, pepper, eggs, and ricotta cheeses in a large bowl.
Place squash in a microwave-safe bowl. Cover and cook on high 5 minutes or until tender.
Coat the bottom and sides of 2 (8-inch-square) baking dishes with cooking spray. Spread 1/2 cup Smoky Marinara in the bottom of one prepared dish. Arrange 2 noodles over sauce; spread 1 cup cheese mixture over noodles. Arrange 1 1/2 cups squash over cheese mixture; spread 3/4 cup sauce over squash.
Arrange 2 noodles over sauce; spread 1 cup cheese mixture over the noodles. Arrange 1 1/2 cups onion mixture over cheese mixture; spread 3/4 cup sauce over spinach mixture.
Arrange 2 noodles over sauce; spread 1 cup Smoky Marinara evenly over noodles. Sprinkle with 1/2 cup Parmesan. Repeat procedure with remaining ingredients in remaining pan. Cover each pan with foil.
Bake at 375° for 30 minutes. Uncover and bake an additional 30 minutes.
To freeze unbaked lasagna: Prepare through Step Cover with plastic wrap, pressing to remove as much air as possible. Wrap with heavy-duty foil. Store in freezer for up to 2 months.
To prepare frozen unbaked lasagna: Thaw completely in refrigerator (about 24 hours). Preheat oven to 375º. Remove foil; reserve foil. Remove plastic wrap; discard wrap. Cover lasagna with reserved foil; bake at 375º for 1 hour. Uncover and bake an additional 30 minutes or until bubbly.