Mix sage, salt, black pepper, 1/2 teaspoon nutmeg, and 1/2 teaspoon cloves together in a small bowl to make a spice blend.
Heat olive oil in a large skillet over medium-high heat. Add mushrooms, onion, garlic, and 1/2 of the spice blend; cook and stir until mushrooms are tender and all moisture has evaporated, about 5 minutes.
Combine 2 cups pumpkin puree, 3/4 cup heavy cream, 1/2 cup Parmesan cheese, and remaining spice blend in a bowl.
Grease a 9x13-inch baking pan with cooking spray. Arrange 4 lasagna noodles in the bottom so they slightly overlap. Cover with 1/2 of the pumpkin mixture and 1/2 of the mushroom mixture. Dot with 1/2 cup ricotta; sprinkle 1/2 cup mozzarella cheese on top. Repeat layers once more. Place remaining 4 noodles on top.
Combine remaining 1 cup pumpkin puree, remaining 3/4 cup heavy cream, 1 dash nutmeg, and 1 dash cloves. Spread on top of noodles. Sprinkle remaining 1 cup Parmesan cheese on top. Dot with butter. Cover with aluminum foil.
Bake in the preheated oven for 20 minutes. Uncover and bake until bubbly, about 15 minutes more.