Boil a large pot of salted water. Add the pasta and cook according to package instructions until al dente. Reserve 1/2 cup of pasta water, then drain the pasta and set it aside.
In a skillet over medium heat, add 2 tablespoons of olive oil. Season the chicken strips with salt and pepper before placing them in the skillet. Cook for about 5-7 minutes or until the chicken is cooked through and lightly golden brown. Remove from heat and set aside.
In a food processor, combine the basil leaves, pine nuts, Parmesan cheese, minced garlic, lemon juice, and 1/2 cup olive oil. Pulse until smooth, scraping down the sides as necessary. If the pesto is too thick, add a small amount of reserved pasta water until desired consistency is reached.
In a large mixing bowl, combine the cooked pasta, chicken, and pesto. Toss well to combine all ingredients. If needed, add more reserved pasta water for a creamier texture.
Serve immediately in pasta bowls, garnished with extra Parmesan cheese and fresh basil leaves if desired.