Bring a large pot of salted water to a boil. Add the spaghetti and cook according to the package directions. Reserve 1/4 cup pasta water, then drain the pasta.
In the meantime, pulse the tuna, breadcrumbs, Parmesan, parsley, garlic, egg, 1/2 teaspoon salt and 1/4 teaspoon pepper in a food processor until combined. Shape the mixture into balls by the tablespoonful.
In a large nonstick skillet, heat the olive oil over medium heat. Brown the meatballs for about 2 minutes per side; remove and set aside. Add the pesto, cream, lemon zest and juice, reserved pasta water and cooked pasta to the skillet and toss until the pasta is evenly coated. Add the meatballs and gently toss. Serve with more Parmesan.