Bring a large pot of lightly salted water to a boil. Cook spaghetti in the boiling water, stirring occasionally until cooked through but firm to the bite, about 12 minutes; drain.
Blend basil, lemon juice, 3 tablespoons olive oil, garlic, and salt in a blender until smooth.
Heat 2 teaspoons olive oil in a skillet over medium heat. Cook and stir sugar snap peas in hot oil until tender, about 5 minutes. Add shrimp and red pepper; continue to cook until the shrimp are bright pink on the outside and the meat is no longer transparent in the center, about 5 minutes. Stir basil sauce into the shrimp mixture and remove from heat; spoon over spaghetti to serve.
