Begin by preheating the oven to 180°C.
Heat olive oil in a pan over medium heat. Add the chicken and season it with salt and pepper. Cook the chicken until it is no longer pink and then set it aside.
In the same pan, sauté the onions, garlic, and mushrooms until the onions become translucent and the mushrooms are cooked.
In a separate pot, melt the butter and then add the flour, stirring until it forms a paste. Gradually add the milk while stirring continuously to avoid lumps. Cook the sauce until it thickens.
Mix half of the mozzarella and Parmesan cheeses into the sauce, stirring until the cheese is melted and fully incorporated.
Assemble the lasagna: Start with a layer of sauce at the bottom of the baking dish, followed by lasagna sheets, then the chicken and mushroom mixture, and another layer of sauce. Repeat these layers.
For the final layer, top it with the remaining mozzarella and Parmesan cheeses.
Place the baking dish in the preheated oven and bake for 45 minutes, or until the top turns golden and bubbly.
Allow the lasagna to rest for 10 minutes before serving.