Bring a large pot of salted water to a boil over high heat. Add 1 teaspoon olive oil. Add the pasta and cook until tender but still firm to the bite, stirring occasionally, about 8 to 10 minutes for dried pasta or 2 to 3 minutes for fresh pasta. Drain pasta.
In a food processor combine the sun-dried tomatoes and basil. Pulse until the mixture is combined. Transfer to a small bowl. Stir in 1/2 cup Parmesan. Set aside.
In a large skillet brown the pancetta until crisp. Remove from the pan using a slotted spoon. Add 1 tablespoon olive oil, onion, and garlic and cook until tender, about 4 minutes. Add asparagus and cook until tender, about 4 minutes. Transfer the mixture to a large bowl. Add the ricotta, salt, and pepper and stir to combine.
Preheat the oven to 350 degrees F. In a 9 by 13-inch baking dish sprinkle some of the sun-dried tomato mixture on the bottom of the casserole dish. Place some lasagna sheets, then half asparagus mixture. Next sprinkle some mozzarella cheese and some of the remaining 3/4 cup Parmesan. Continue for 1 more layer. Top with lasagna sheets, some sun-dried tomato mixture, mozzarella, and Parmesan. Dot the top with butter. Bake until the ingredients are warm and the cheese is melted, about 25 minutes.