Preheat the oven to 375°F.
Place the asparagus in a microwave-safe dish with 1/4 cup of water, cover, and steam for 3 minutes or until tender, then drain and set aside.
Melt butter in a 12-inch skillet over medium-high heat, add the chicken, and cook for 3 to 4 minutes per side until browned and cooked through.
Transfer the chicken to a greased casserole dish, top with the steamed asparagus, and cover to keep warm.
Add onions and mushrooms to the skillet and sauté until tender.
Reduce the heat to medium, add broth, cream, salt, pepper, thyme, Dijon, mayonnaise, and lemon juice, then whisk and bring to a simmer.
Cook the sauce for 8 to 10 minutes, stirring frequently until reduced and thickened, then stir in the cheese.
Pour the mixture over the casserole, sprinkle with the remaining cheeses, and bake for 30 minutes until bubbly and the chicken is done.
