Bring a large pot of well-salted water to a boil.
Using a zester tool (called a channel knife), zest the lemon into thin strips, or, using a vegetable peeler, shave off the zest, then slice into very thin strips. Juice the lemon to get 2 Tbs. juice.
Heat 1/4 cup of the oil in a 10-inch straight-sided sauté pan over medium heat. Add the capers and cook until they start to brown and get crisp, 3 to 5 minutes. Stir in the lemon zest and cook until it starts to crisp and curl up, about 1 minute. Using a slotted spoon, transfer the capers and lemon zest to a plate lined with a paper towel—it’s fine if a few capers remain in the pan.
Reduce the heat to medium low, add the garlic to the remaining oil in the pan and cook, stirring, until it browns lightly but doesn’t burn, 2 to 3 minutes. Add the tuna and red pepper flakes and cook until the tuna just heats through, about 2 minutes. Remove from the heat.
Meanwhile, cook the fettuccine in the boiling salted water, stirring often, until it’s just tender to the tooth (see the package for cooking time). Reserve 1/2 cup of the pasta water and drain the pasta.
Return the sauté pan to medium heat. Add the drained pasta, 1/4 cup of the reserved pasta water, 2 Tbs. of the lemon juice, and the remaining 2 Tbs. olive oil. Cook, tossing and stirring, for 1 to 2 minutes to blend the flavors. If the pasta isn’t tender, add the remaining cooking water and continue to cook and stir until done. Season to taste with salt, pepper, and more lemon juice.
Serve immediately, drizzled with a little olive oil and sprinkled with the capers, lemon strips, parsley, and a few grinds of black pepper.