Bring a large pot of salted water to a boil and add the spaghetti. Cook according to the package directions until al dente, then reserve a small cup of the pasta water before draining. That starchy water comes in handy if the sauce needs loosening later.
While the pasta cooks, warm two tablespoons of olive oil in a large skillet over medium heat. Add the garlic and red pepper flakes, stirring for about a minute until fragrant. Keep the heat moderate so the garlic doesn't turn bitter.
Add the bell pepper and cherry tomatoes to the skillet and cook for four to five minutes, pressing gently so the tomatoes start to burst and release their juices. This forms the light, chunky sauce that coats the noodles later.
Stir in the olives, then add the spinach and basil. Cook for about a minute, just until the spinach wilts down. This step goes fast, so keep everything moving in the pan.
Add the drained spaghetti straight into the skillet along with the remaining olive oil, lemon juice, and zest. Toss everything together, adding a splash of the reserved pasta water if the mixture looks dry.
Taste and adjust the salt, pepper, and lemon as needed. Finish with freshly grated Parmesan if using, then serve right away while everything is still warm and vibrant.