Preheat the oven to 375 degrees F (190 degrees C). Grease a casserole dish or 9x13-inch pan.
Slice or cube chicken and season lightly with 1/2 teaspoon salt and 1/8 teaspoon pepper.
Bring a large pot of lightly salted water to a boil. Cook pasta at a boil, stirring occasionally, for 6 minutes. Drain, cover, and set aside.
Heat butter and olive oil in a large pan over medium-high heat. Add chicken and cook until lightly browned, about 5 minutes. Add wine and cook, 1 to 2 minutes. Add garlic and lemon juice and cook, 1 to 2 minutes. Don't allow garlic to brown.
Reduce heat to medium-low and add cream cheese, stirring until melted and blended. Add flour to sour cream, mix well, and stir into the pan. Add chicken stock, parsley, thyme, red pepper, salt, and pepper. Bring to a simmer until slightly thickened. Add more stock if sauce is too thick. Remove from heat.
Add 1/2 cup Parmesan and lemon zest, stir well. Taste and adjust seasoning. Add partially cooked pasta and blend well. Pour into the prepared baking or casserole pan and sprinkle with remaining Parmesan cheese.
Bake, covered, in the preheated oven for 15 minutes. Uncover and continue to bake until lightly browned, 7 to 10 minutes more.
