Brush an 8-inch square baking dish with oil; set aside. In a medium bowl, mix squash puree with sage, 1 1/2 teaspoons salt, and 1/4 teaspoon pepper. In another bowl, mix ricotta with 1/2 cup Parmesan, 1 teaspoon salt, and 1/4 teaspoon pepper. Set aside.
Lay 2 lasagna noodles in the bottom of prepared dish; spread with half the squash mixture.
Layer with 2 more noodles, and spread with half the ricotta mixture. Repeat layering with remaining noodles and mixtures.
Sprinkle top (ricotta mixture) with remaining 1/2 cup Parmesan.
Cover baking dish with foil; place on a rimmed baking sheet.
Bake until lasagna is heated through, about 45 minutes; remove foil, and continue baking until golden on top, 20 to 25 minutes more.
