Start by bringing a large pot of salted water to a boil. Add the linguine or spaghetti and cook according to the package instructions until al dente, about 8 to 10 minutes. Reserve 1/2 cup of pasta water, then drain and set aside.
While the pasta cooks, heat olive oil and 2 tablespoons butter in a large skillet over medium-high heat. Add shrimp in a single layer, season with salt and pepper, and cook about 2 minutes per side until pink and opaque. Remove shrimp and set aside.
Reduce heat to medium. Add minced garlic and red pepper flakes to the skillet. Sauté about 1 minute until fragrant but not browned. Stir in lemon juice and lemon zest, scraping up browned bits for flavor.
Return shrimp to skillet with remaining 2 tablespoons butter. Toss in cooked pasta and mix gently. Add reserved pasta water as needed to loosen sauce and coat noodles evenly.
Turn off heat and sprinkle chopped fresh parsley over the pasta. Toss to combine, adjust seasoning with salt and pepper if needed, and serve immediately.