Preheat oven to 400°F. Cook lasagna noodles in boiling salted water until just al dente, about 8 minutes. Drain well and transfer noodles to a baking pan. Toss the noodles with 1 tablespoon of the olive oil to prevent them from sticking together.
Heat remaining 2 tablespoons olive oil in a large skillet over medium-high. Add sausage; cook about 4 minutes, stirring occasionally, until lightly browned. Add onion, reduce heat to medium, and cook 4 minutes, stirring occasionally, until softened. Add collard greens, and cook about 8 minutes, stirring frequently, until wilted and liquid has evaporated. Add garlic and cook until fragrant, about 1 minute. Season with 1 teaspoon of the salt and 1/2 teaspoon of the pepper. Remove from heat and cool slightly.
In a medium bowl, stir together 1 teaspoon of the salt, remaining 1/2 teaspoon pepper, pumpkin puree, heavy cream, nutmeg, and cayenne pepper. In another bowl, stir together remaining 1/2 teaspoon salt, ricotta, eggs, 1 1/2 cups of the Parmesan, and 1 cup of the Fontina.
Coat a 9- x 13-inch (3-quart) broiler-proof baking dish with cooking spray. Spoon 1/2 cup of the pumpkin mixture in bottom of dish; spread in an even layer. Arrange 3 or 4 lasagna noodles in the dish over pumpkin mixture, overlapping slightly. Spread half of the remaining pumpkin mixture over the noodles in an even layer. Top with half of the sausage mixture and another layer of 3 to 4 noodles. Spread half of the ricotta mixture over noodles. Repeat layering with noodles, remaining pumpkin mixture, remaining sausage mixture, another layer of noodles, and remaining ricotta mixture.
Cover lasagna with foil and bake until bubbly around the edges and thoroughly heated in center; about 50 minutes. Remove from the oven and uncover. Preheat broiler. Sprinkle remaining 1/2 cup of Parmesan and remaining 1 cup Fontina on top of lasagna and broil about 4 inches from heat source until browned, about 4 minutes. Let stand 15 minutes before serving.