According to the Oxford English Dictionary, lady derives from the Old English words for "hláf", loaf and "dig", to knead.
Despite what appears to be clear etymological evidence, the editors of the OED state that this is not plausible with regard to sense. Yet attempts to explain "lady" as the feminization of "lord" is problematic.
I find this difficulty on the editors' part puzzling. Why is it so difficult to comprehend the lady of the house as a kneader of loaves? It is only relatively recently in Western history (last 500 years or so?) that a man could, by his own efforts and management of resources, support idle able-bodied members of household. An idle wife was and often still is a status symbol.
Prior to this, the lady of the house was the housekeeper in a very literal sense, the household manager. She was responsible for the maintenance and distribution of the household's production. She kept inventory of the house's stores. She directed the servants in their household tasks and duties. It only makes sense, that as the lady of the house, she should take responsibility for the production of its most important food-stuff, bread. Hence, loaf-kneader, thus lady.
Had a very interesting & informative conversation with Gritchka about etymological problems of "lady". Seems OED is not the final authority. I am hoping Gritchka will summarize her findings here.