Whisk oil, lemon zest and juice, garlic, and 1/2 teaspoon salt together in small bowl, then stir in Parmesan until thick and creamy.
Melt 2 tablespoons butter in 12-inch nonstick skillet over medium heat. Pat scallops dry with paper towels and season with salt and pepper. Add scallops in single layer and cook until scallops are firm, about 3 minutes; transfer to bowl and cover.
Meanwhile, bring 4 quarts water to boil in large pot. Add pasta and 1 tablespoon salt and cook, stirring often, until al dente. Reserve 1/2 cup cooking water, then drain pasta and return it to pot.
Stir in olive oil mixture, scallops with any accumulated juices, remaining 2 tablespoons butter, and basil and toss to combine. Add reserved cooking water as needed to adjust consistency. Season with salt and pepper to taste. Serve.