Place 4 quarts of water in a large pot, season with salt and bring to a boil.
Wash the zucchini and trim the ends, then grate them on the largest side of a box grater and set aside.
In a large saucepan, heat the oil and butter and sauté the shallot and celery over medium heat, stirring, until the vegetables soften and begin to turn translucent. Add the minced garlic and continue cooking for another minute. Add the zucchini to the pan and sauté until the zucchini begins to soften and wilt.
In the meantime, add the pasta to the boiling water and stir occasionally as the pasta cooks.
Season the vegetables with salt and pepper. When the pasta is almost al dente, add the lemon juice, 1/4 of a cup of the pasta cooking water and the cheese to the pan, stirring to melt the cheese. Stir in the parsley and basil and let the mixture simmer gently for a moment or two.
Drain the pasta, reserving some of the cooking water in case it is needed; add the pasta to the pan with the sauce and toss to coat it completely. Let the pasta cook in the pan for a minute, adding a splash of the reserved cooking water if the sauce seems too tight. Transfer to a warm bowl and serve immediately.