Start by preparing the ingredients.Peel the carrots and cut them into very small cubes.Peel and finely chop the onion with a knife. Peel and crush the garlic cloves.Cut the celery stalks into small pieces.Cut the mushrooms into small cubes.
In a Dutch oven or cast iron skillet, pour the oil and add the onion, carrots, celery, and crushed garlic cloves. Cook for 2 minutes, stirring constantly.Then add the diced mushrooms and sauté for another 10 to 20 minutes, until softened.Add the wine, tomato paste, and tomato puree, then mix well.Add the herbs (thyme, bay leaf, rosemary), sugar, and paprika. Season with salt and pepper, and stir.Cook, covered, over low heat for at least 1 hour. Remember to stir occasionally.
Add the drained and rinsed lentils and lemon juice. Adjust the seasoning if necessary and stir.
For the cheese bechamel sauce
While the Bolognese simmers, prepare the béchamel sauce.In a large saucepan, melt the butter over medium heat with the crushed garlic.Add the flour, whisk, and let the roux cook for 3 to 5 minutes, stirring constantly.Pour in the milk (all at once), stir over medium heat, and cook until the sauce thickens.It should be quite thick.
Remove from heat, add a little salt (or not, as there will be cheese), pepper, and a pinch of nutmeg. Mix well.Add the grated cheese and mix again until well incorporated.
For assembly
Preheat your oven to 180°C and oil the bottom and sides of a large baking dish (approximately 30x25 cm).
Place a few spoonfuls of Bolognese sauce on the bottom of the dish and arrange the lasagna sheets to form a first layer.Cover with Bolognese sauce, then bechamel sauce and grated cheese.Repeat the process (lasagna, Bolognese, bechamel sauce, cheese) and finish by generously covering the lasagna sheets with béchamel sauce and grated cheese. This will create about three layers.
Bake for 30 to 35 minutes, or until golden brown. Serve warm with a green salad.