Preheat oven to 350 degrees F (175 degrees C). Lightly grease a 2 quart baking dish.
Melt butter in a medium sized pot over low heat. Saute the lobster meat in butter until it starts to change color. Do not cook too long or too fast, or the lobster meat will toughen. With a slotted spoon, remove lobster meat from pan and set aside.
To the remaining butter in the pot, stir in the flour, dry mustard, salt and pepper. Gradually whisk in cream and milk. Cook, stirring constantly, until thickened, about 5 minutes. Return lobster meat to the pot. Tear the bread into small pieces and stir into the mixture. Pour into prepared baking dish.
Bake in preheated oven for 20 to 25 minutes or until bubbly and delicately browned.