Bring a large pot of lightly salted water and 1 tablespoon olive oil to a boil. Cook linguine at a boil until tender yet firm to the bite, about 11 minutes.
Heat remaining 2 tablespoons olive oil in a large, deep skillet over medium-high heat. Add onion; cook and stir until softened and translucent, 2 to 3 minutes. Stir in garlic and cook until fragrant, about 1 minute. Pour in juice of 2 lemons and stir well. Add asparagus; cook until softened, 2 to 3 minutes. Pour in white wine. Reduce heat; simmer until thickened and reduced, 5 to 7 minutes. Stir in shrimp; cook until they are bright pink on the outside and the meat is opaque, 4 to 5 minutes.
Mix in remaining lemon juice and capers until you have reached your desired flavor. Season with Italian seasoning, salt, and pepper.
Toss cooked pasta with sauce. Serve topped with Parmesan cheese.
