In a small saucepan, bring 2 cups water to a boil over high heat. Off the heat, add the morels, cover, and soak until soft and rehydrated, 30 minutes. Lift them out with a slotted spoon and gently press on them with another spoon to squeeze excess liquid back into the pot. Cut any large ones in half, and set the mushrooms aside. Strain the soaking liquid through a sieve lined with a coffee filter and return it to the (rinsed) saucepan. Over medium-high heat, reduce the soaking liquid to 1/4 cup, about 10 minutes.
Melt the butter in a 3-quart saucepan over medium heat. Add the shallots and cook, stirring often, until soft and golden brown, 2 minutes. Add the garlic and cook for 1 minute, then add the morels. Reduce the heat to low and cook, stirring often, until heated through, about 2 minutes. Add the Marsala and increase the heat to bring to a simmer. Cook until the mixture begins to dry out, 8 to 10 minutes. Add the reduced soaking liquid, cream, and 1/2 tsp. salt. Simmer until the sauce thickens slightly, about 10 minutes. Add the lemon juice and herbs, and season to taste with salt and pepper. (You can keep the sauce warm for up to 30 minutes before serving.)