Bring a large pot of lightly salted water to a boil. Add penne and cook, stirring occasionally, until tender yet firm to the bite, about 11 minutes.
Empty tuna into a bowl and mash with a fork while pasta is cooking. Mix with 2 tablespoons olive oil, basil, lemon juice, lemon zest, salt, and pepper.
Heat the remaining 2 tablespoons olive oil in a large skillet and fry the anchovies for 3 minutes. Add capers and garlic; cook, stirring constantly, for an additional 3 minutes. Add tuna mixture and tomatoes; simmer sauce for about 5 minutes.
Drain pasta and add to the sauce. Mix well. Stir in parsley before serving.
