Heat oil in a large skillet over medium-high and cook chicken cubes until browned on all sides.
Transfer chicken to a plate and set aside.
In the same skillet melt butter over medium-low heat, then whisk in flour until smooth.
Remove the pan from heat and slowly whisk in the milk.
Return pan to heat and whisk constantly while simmering until sauce is smooth and thick. Remove mushrooms from water (they should have soaked about 20 minutes) to a cutting board.
Whisk mushroom soaking liquid into the bechamel sauce until smooth.
Remove from heat, and stir in salt, nutmeg, sage and thyme. Coarsely chop mushrooms and stir into the sauce. Stir the cooked chicken cubes in there, too.
Build lasagna by spreading a thin layer of sauce in the bottom of an 9" x 13" baking pan. Layer three lasagna noodles, then spread with the ricotta cheese and ⅓ of the sauce.
Layer three more lasagna noodles, then the mozzarella, then ⅓ more sauce. For the final layer use the remaining three lasagna noodles, the remaining sauce, and then the Parmesan cheese.
Bake in the center of the oven for about 60 minutes, until bubbling and golden on top. Let stand for 10-15 minutes before slicing into squares.