Bring a large pot of salted water to a boil. Add the whole wheat spaghetti and cook according to package instructions until al dente, reserving 1/2 to 2/3 cup of the pasta cooking water before draining the pasta.
While the pasta cooks, heat the olive oil in a skillet over medium heat.
Add the minced garlic to the skillet and sauté until fragrant, about 1 minute—do not let it brown.
Stir in the drained tuna, drained capers, and lemon juice, breaking up any large tuna pieces; cook until heated through, about 2 minutes.
Add the cooked spaghetti to the skillet with about 1/2 cup of the reserved pasta water and toss to coat, adding up to 2/3 cup total if needed to loosen the sauce.
Allow the pasta water to reduce slightly while tossing so the sauce clings to the pasta.
Season with salt and black pepper to taste, stir in the chopped parsley, and adjust lemon juice if desired.
Serve immediately, topped with shredded or grated Parmesan and additional parsley if using.