Old English hlǣfdīge contains bread and a kneader element. Middle English carried the word toward lady.
Collins directly glosses dīge; Merriam-Webster connects -dige with a related kneader word. This is a word history, not a claim about the duties of every title-holder.
Sources
- Merriam-Webster: lady
The compound includes hlāf and a kneader-related second element.
- Collins: lady
The entry explicitly glosses dīge as kneader.
- Online Etymology Dictionary: loaf
Also built on Old English *hlaf* "bread": lord
- Online Etymology Dictionary · lady
Meanings of the older forms on the word path.