Cook spaghetti according to package instructions until al dente. Reserve 1/4 cup of pasta water, then drain the pasta.
While pasta cooks, heat 2 tablespoons of olive oil in a large skillet over medium-high heat.
Add shrimp and season with salt and pepper. Cook for 1-2 minutes on each side until shrimp are pink and opaque. Remove from skillet and set aside.
In the same skillet, add remaining tablespoon olive oil and garlic. Sauté for about 1 minute until fragrant.
Add lemon zest, lemon juice, and reserved pasta water to the skillet. Let simmer for 1-2 minutes.
Return shrimp to the skillet, toss to coat with the lemon garlic sauce, then add the drained spaghetti. Mix well.
Garnish with fresh parsley and serve hot.