Preheat the oven to 375 degrees F.
Lift the morels carefully from the hot water in order to leave any grit behind in the liquid. Rinse a few times to be sure all the grittiness is gone. Discard the liquid and dry the morels lightly with paper towels. Set aside.
Sprinkle the chicken breasts with salt and pepper. Dredge them in flour and shake off the excess. Heat half the clarified butter in a large saute pan and cook the chicken in 2 batches over medium-low heat until browned on both sides, 8 to 10 minutes. Remove to an ovenproof casserole.
Add the rest of the clarified butter to the pan along with the shallots, drained morels, and garlic. Saute over medium heat for 2 minutes, tossing and stirring constantly. Pour the Madeira into the pan and reduce the liquid by half over high heat, 2 to 4 minutes. Add the creme fraiche, cream, lemon juice, 1 teaspoon salt, and 3⁄4 teaspoon pepper. Boil until the mixture starts to thicken, 5 to 10 minutes. Pour the sauce over the chicken and bake for 12 minutes, or until the chicken is heated through. To make ahead, refrigerate the chicken and sauce in the casserole and reheat slowly on top of the stove.
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