Heat oil in a large pot. Add onion, celery and carrot. Sautee until softened, about 5 minutes.
Add garlic and cook for another minute.
Add beef, and increase heat to high. Cook until browned. Sprinkle with cinnamon and thyme.
Stir in tomato sauce, and season with salt and pepper. Bring to a simmer, then turn down the heat, cover the pan and let cook for an hour. Stir occasionally.
To prepare béchamel sauce, melt butter in a sauce pan. Stir in flour and cook, stirring constantly, until the paste cooks and starts bubbling. Slowly add in the warm milk while stirring. Reduce heat to low, and keep cooking until the sauce begins to thicken. Season with salt and pepper. Continue cooking and stirring until the right consistency has developed and lump free. Remove from heat.
Preheat oven to 380F. Cook the lasagna in boiling water with a little oil for about 8 minutes, until al dente.
Lightly grease the baking pan. Layer three lasagna sheets on the bottom, then spread a third of the bolognese sauce on top, followed by béchamel sauce. Sprinkle with cheese. Repeat until the final layer of lasagna sheets is placed. Top with the remaining béchamel sauce and cheese.
Cover the pan with aluminium foil, and bake in the oven for 45 minutes, until the sauce is bubbling. Remove the aluminium foil, cook for another 8 minutes until the top begins to get lightly browned. Remove from oven and let cool for 10 minutes before serving.