Combine butter, shortening, brown sugar, molasses, and eggs; beat well at medium speed of an electric mixer.
Combine flour and the next 6 ingredients; stir well. Add the flour mixture to the molasses mixture, stirring well. Stir in the boiling water.
Pour the batter into a greased 13 x 9 x 2 inch baking pan. Bake at 350 degrees for 30 to 40 minutes or until a wooden pick inserted in the center comes out clean. Let cool in the pan on a wire rack.
For the sauce, combine the sugar and beaten egg in the top of a double boiler, and stir well. Add the butter boiling water, and lemon juice, and stir well. Bring water in the bottom of the double boiler to a boil; reduce heat to low, and cook, stirring constantly, until the mixture is smooth and slightly thickened. Serve cake with warm lemon sauce.