Bring a large pot of heavily salted water to a boil. Cook the spaghetti according to the package directions, stirring often as it cooks to keep it from sticking. Reserve about 1 cup of the starchy cooking liquid, drain the pasta and rinse with hot water.
Place the shrimp on a baking dish, drizzle with 1 tablespoon olive oil, ½ teaspoon salt, and ½ teaspoon pepper. Toss to coat and spread in an even layer. Roast in the oven for 6 – 8 minutes or until the shrimp are pink and just cooked through. Do not over-cook.
In a large skillet, heat the remaining olive oil and the butter over medium heat until the butter melts. Add the garlic and cook for 30 seconds. Add the pasta to the pan along with the zest and juice of the lemons, the parsley and red pepper flakes. Stir in some of the reserved pasta cooking water until saucy. Add the shrimp and toss. Season to taste with more salt and pepper if desired.