I've searched to find out who Lady Derby is but as of this date, I have not found any information about her. I did however find out that the soap was also called Almond Soap. The earliest use of this recipe I've found is the one below. I did however find many Lords and Ladys of Derby in England over the years. To which Lady this recipe comes from, is unknown to me at the moment.
Below is from The New Families Receipts book ©1810
To make Lady Derby's Soap.
Two ounces of bitter almonds blanched, one ounce and a quarter of tincture of benjamin, one pound of good plain white soap, and one piece of camphire the size of a walnut. The almonds and camphire are to be beaten in a mortar until they are completely mixed; then work up with them the tincture of benjamin. The mixture being perfectly made, work the soap into it in the same manner. If the smell is too powerful of the camphire and tincture of benjamin, melt the soap by the fire, and the perfume will go off. This soap has been tried by many persons of distinction, is excellent in its qualities for cleansing the skin, and will be found greatly to assist the complexion, the ingredients being perfectly safe, and free from those jjernicious properties that are mostly incorporated with other soap.