Preheat the oven to 400℉. Spray a 9x13-inch baking pan with nonstick spray.
PREPARE THE SAUCE:
Heat olive oil and butter in a medium skillet over medium heat. Whisk in the flour and stir until lightly browned. Slowly whisk in the milk. Keep whisking until the milk is warmed and has thickened slightly. Whisk in the cheeses, thyme, lemon zest/juice and salt and pepper. Set aside for later.
PREPARE THE VEGETABLES:
While the spaghetti is cooking, prepare the vegetables. In a very large, nonstick skillet heat the olive oil over medium heat. Add the garlic and stir for 1 minute. Add broccoli, carrot, and bell pepper. Stir and cook until slightly softened, 4 to 5 minutes. Turn off the heat. Add spaghetti to the skillet and gently toss the vegetables with the spaghetti. Add the chicken, and then add the sauce. Toss to combine. Transfer the pasta-vegetable mixture to the prepared baking pan, spread the cut tomatoes on top, and sprinkle with salt and pepper. Cover the pan with foil. Bake for 30 minutes. Remove the foil and sprinkle cheeses on top. Squeeze the juice from 1/2 lemon on top of the cheeses. Return to the oven and bake until the cheeses are melted and the tomatoes are wilted- about 10 minutes.