Bring a large pot of salted water to a boil.
Add pasta and cook according to package directions until al dente.
Reserve 1/4 cup of the pasta water, then drain the pasta and set aside.
In a food processor or blender, add the basil leaves, Parmesan cheese, nuts, and garlic.
Pulse several times until the mixture is chopped well.
With the processor running, slowly stream in the olive oil until the pesto is smooth.
Add the lemon juice, salt, and pepper, then blend again until fully combined.
Taste the pesto and adjust seasoning as needed.
Place the drained pasta in a large mixing bowl.
Add the pesto and toss to coat the pasta evenly.
If the sauce is too thick, stir in a bit of the reserved pasta water until creamy.
Serve warm, topped with extra Parmesan or fresh basil if desired.