Bring a large pot of salted water to a boil. Cook spaghetti 2 minutes less than al dente directions. Reserve ¼ cup of the pasta water, drain the pasta, and set aside.
Add olive oil and butter to a medium skillet on medium-high. Once the pan is hot and butter melted, add the onion, peppers, and mushrooms. Cook until tender, about 5 minutes. Add the garlic and crushed red pepper, and cook an additional minute.
Add the garlic and crushed red pepper, and cook an additional minute. Stir in the broth, lemon juice, cream, and parmesan, scraping up any bits from the bottom of the pan. Simmer 5 minutes.
Fold in the drained pasta and incorporate with the sauce. Add the reserved pasta water, and simmer 3 minutes.
Cut the chicken into large pieces and fold into the pasta. Plate, and garnish as desired.