Soak morels in 3 cups very hot water for 30 minutes to re-hydrate. Lift them carefully from the hot water in order to leave any grit behind in the liquid. Discard the liquid, and dry the morels lightly with paper towels. Cut morels crosswise into 1/4-inch to 3/8-inch wide slices and set aside. Sprinkle chicken breasts with salt and pepper. Dredge chicken in flour, and shake off excess. Heat half the clarified butter (1/8 cup) in a large saute pan, and cook the chicken over medium heat for about 8 to 10 minutes. Flip the chicken and brown on the second side, 4 to 5 minutes more. Remove to an ovenproof casserole dish. Add the rest of the clarified butter (the other 1/8 cup) to the same saute pan, add the morels and button mushrooms, and cook gently over low heat for 2 minutes. Then add the Madeira and reduce the liquid by half.
Preheat oven to 375 degrees F.
When the liquid is reduced, add the beef stock and heavy cream and bring to a gentle boil. Let the mushroom sauce cook until mixture starts to thicken, about 5 to 10 minutes. Pour the sauce over the chicken and bake covered in the oven until done, about 25 to 35 minutes. Sprinkle with fresh lemon juice and serve.