In a large bowl, whisk the oil, Parmesan cheese, lemon juice, salt, and pepper to blend. Set the lemon sauce aside. (The sauce can be made up to 8 hours ahead. Cover and refrigerate. Bring to room temperature before using.)
Meanwhile, bring a large pot of salted water to a boil. Add the spaghetti and cook, stirring occasionally, until tender but still firm to the bite, about 8 minutes. Drain, reserving ½ cup of the cooking liquid.
Add the spaghetti to the lemon sauce, and toss with the basil and lemon zest. Toss the pasta with enough reserved cooking liquid, ¼ cup at a time, to moisten. Season the pasta with more salt and pepper to taste. Transfer to bowls and serve.