Preheat grill to medium-high heat. Cook the pasta according to the package instructions. Drain and put into a large bowl.
Season the chicken with Italian seasoning, salt, and pepper. Place the asparagus in a single layer on a baking sheet lined with foil. Drizzle with olive oil, salt, and pepper, toss to coat.
Grill the chicken for about 4-6 minutes, flip and grill for an additional 4-6 minutes, or until internal temperature reaches 160-165 degrees. Allow chicken to rest 5 minutes before slicing.
While chicken is cooking, place the prepared asparagus onto the grill grates horizontally. Grill for 2 minutes, flip and grill an additional 1-2 minutes. Cut into approximately 2-inch pieces.
Add the chopped chicken and asparagus to the bowl with the pasta. Add in the pesto, lemon juice, and shredded parmesan cheese. Season with salt and pepper and toss everything together until coated. Taste for seasoning. Garnish with toasted pine nuts and chopped fresh basil. Serve warm or cold.