Bring a large pot of salted water to a boil. Cook the spaghetti according to the package directions until al dente.
Meanwhile, make the sauce: In a small food processor or blender, combine the basil, chives, dill, garlic, zest, oil, 1 1/2 teaspoons salt and the pepper. Blend until smooth. Taste and add more salt, if desired. Set the herb sauce aside.
Drain the pasta and, while it's still in the colander, toss with the lemon juice. Transfer to a large bowl and pour in the herb sauce. Toss thoroughly until the pasta is completely coated.
Serve family-style warm or at room temperature with freshly grated Parmesan, if desired.