Cook the pasta in a large pot of boiling salted water until tender but still firm to the bite, stirring occasionally, about 8 minutes. Meanwhile, whisk the oil, Parmesan, and lemon juice in a large bowl to blend.
Drain the pasta, reserving 1 cup of the cooking liquid. Toss the pasta with the lemon sauce, and the reserved cooking liquid, adding 1/4 cup at a time as needed to moisten. Season with salt and pepper. Garnish with lemon zest and chopped basil.