Whisk the oil, 2 teaspoons of the lemon juice, garlic, shallot, ¼ teaspoon salt, and ¼ teaspoon pepper together in a large bowl. Add the tomatoes and gently toss to combine; set aside. Do not marinate for more than 45 minutes.
While the tomatoes are marinating, place the mozzarella on a plate and freeze until slightly firm, about 10 minutes. Bring 4 quarts water to a boil in a stockpot. Add the pasta and 1 tablespoon salt and cook until al dente. Drain well.
Add the pasta and mozzarella to the tomato mixture and gently toss to combine. Let stand 5 minutes. Stir in the basil, season with salt and pepper to taste, and additional lemon juice or sugar, if desired. Serve immediately.