Preheat the oven to 375°F (190°C).
Bring 4 quarts of water and 1 tablespoon salt to a boil in a large stock pot. Add the lasagna noodles and cook until just al dente, about 10 minutes. Drain and rinse with cold water to prevent sticking; set aside.
In a large saucepan or Dutch oven over medium-high heat, warm the olive oil until shimmering. Add the sliced mushrooms, chopped onion, and 1/2 teaspoon salt. Cook until the mushrooms have released most of their liquid, about 10 minutes.
Stir in the minced garlic and cook until fragrant, about 30 seconds. Add the squeezed spinach, crushed tomatoes, tomato sauce, sugar, dried basil, Italian seasoning, and fennel seeds. Simmer uncovered, stirring occasionally, for 15 minutes. Taste and season with additional salt and freshly ground black pepper as desired (recipe suggests about 1½ teaspoons salt total and ½ teaspoon pepper).
Meanwhile, in a large bowl combine the ricotta cheese, egg, dried parsley, and 1/2 teaspoon salt; mix until smooth and chill until ready to assemble.
Spoon 2 cups of the tomato-mushroom sauce into the bottom of a 9x13-inch baking dish. Arrange a single layer of cooked noodles over the sauce.
Spread a heaping 2/3 cup of the ricotta mixture over the noodles, then top with about 1½ cups (approximately 5 ounces) of shredded mozzarella and sprinkle with 1/3 cup grated Parmesan.
Spoon 2 cups more sauce over the cheese, then repeat the noodle, ricotta (heaping 2/3 cup), mozzarella (1½ cups), and Parmesan (1/3 cup) layers. Repeat once more to make a total of three layers.
Spray a large piece of aluminum foil with nonstick spray and cover the baking dish. Bake covered for 15 minutes, then remove the foil and bake an additional 25 minutes, or until the lasagna is hot and bubbly.
Let the lasagna cool for at least 10 minutes before slicing and serving.