Preheat the oven to 375°F (190°C).
Bring a large pot with 4 quarts of water and 1 tablespoon salt to a boil. Add the lasagna noodles and cook until just al dente, about 10 minutes. Drain and rinse with cold water to stop cooking and prevent sticking.
Heat 2 tablespoons olive oil in a large saucepan or Dutch oven over medium-high heat. Add the sliced mushrooms, chopped onion, and 1/2 teaspoon salt. Cook, stirring occasionally, until the mushrooms release most of their liquid and the mixture is browned, about 10 minutes.
Add the minced garlic and cook until fragrant, about 30 seconds. Stir in the drained spinach, crushed tomatoes, tomato sauce, 2 tablespoons sugar (or to taste), 1 1/2 teaspoons dried basil, 1 teaspoon Italian seasoning, and 1 teaspoon fennel seeds. Simmer uncovered, stirring occasionally, for 15 minutes. Taste and season with additional salt and freshly ground black pepper as desired; the recipe suggests about 1 1/2 teaspoons salt and 1/2 teaspoon pepper total.
In a large bowl, combine the ricotta cheese, egg, 2 teaspoons dried parsley, and 1/2 teaspoon salt. Mix until smooth and chill while the sauce finishes.
Spread 2 cups of the sauce in 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 1 1/2 cups (≈5 ounces) shredded mozzarella and 1/3 cup grated Parmesan.
Spoon 2 cups of sauce over the cheese, then repeat the noodle, ricotta (heaping 2/3 cup), mozzarella (1 1/2 cups), and Parmesan (1/3 cup) layers two more times for a total of three layers.
Spray a large piece of foil with nonstick spray and cover the baking dish. Bake covered for 15 minutes. Remove the foil and bake for 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.