Peel and finely chop onion, garlic and carrot. Slice mozzarella. Fry ground meat in hot oil until crumbly. Briefly saute onions, tomato paste, garlic and carrot and sprinkle with flour. Deglaze with broth and let simmer about 15 minutes. Occasionally stir and season with salt and pepper.
Melt butter in a pot. Stir in flour and fry briefly. Gradually pour in milk while stirring, season with salt and pepper and let béchamel sauce simmer over low heat for about 5 minutes while stirring. Add thyme.
Preheat oven to 200°C (approximately 400°F.)
Put some béchamel sauce into baking dish and cover with lasagna sheets. Fill dish with alternating layers of ground meat, bechamel sauce and lasagna noodles until all ingredients are used. Drizzle bechamel sauce on top of lasagna.
Top lasagna with Mozzarella slices and sprinkle with Parmesan.
Bake lasagna in preheated oven for about 40 minutes until golden brown. If lasagna is too dark, cover with aluminum foil.
Serve lasagna with salad at will.