In a large pan over medium heat, heat oil. Add garlic and cook until fragrant, 1 minute. Add anchovies and cook until fragrant, another minute. Add tomatoes, olives, capers, and red pepper flakes. Bring to a boil, then reduce heat and let simmer, 15 minutes.

Meanwhile, bring a large pot of salted water to a boil. Add spaghetti and cook al dente; drain – reserving some of the pasta water. Toss spaghetti in sauce. Mix well, adding the reserved pasta water, lemon zest and juice Sprinkle with parsley, basil and Parmesan and serve.