Grate lemon peels to yield 1 tablespoon of lemon zest. Juice the lemons to yield 1/2 cup of fresh lemon juice. Whisk together the oil, Parmesan cheese, lemon juice, salt and pepper in large bowl.
Meanwhile, cook pasta according to the package instructions. Drain, reserving 1 cup of the cooking water.
Add the spaghetti to the lemon sauce, and toss with the basil and lemon zest. Season the pasta with salt and pepper to taste.