There are two related problems with the idea that Old English
hlæfdíge means 'loaf
kneader'. I've once more read through the
OED article on
lady and made notes. What they actually suggest is
hláf 'loaf' + root
díg- 'to knead', followed by the progression of forms (
lefdi, levede, lavedi etc.), with eventual loss of
v, and
lady appearing in the fourteenth century, and under it this comment:
The etym. above stated is not very plausible with regard to sense; but the attempts to explain hlæfdíge as a deriv. of hláford are unsatisfactory
And then they give various good reasons why it couldn't be from hláford-íge where hláford is lord (loaf-ward; this etymology is clear), and -íge is some kind of feminine ending: because there is no such ending.
So assuming the first part of hlæfdíge is from 'loaf', what is this -díge bit? Because no such word or ending is known in the rest of the Old English language. Now Old English is known from texts, and is finite; the real Anglo-Saxon speakers must have had hundreds or even thousands of words that haven't survived on parchment, so this díge could be one of them. If it is, what does it mean?
We don't know for sure. The known words it looks closest to are those related to the idea of kneading: thus the root díg- they mention. But resembling a word meaning 'knead' doesn't make it into a word meaning 'kneader'.
For one thing, we already have that word. You know Susan Dey from The Partridge Family? The surname Dey is from the obsolete Middle English word dey, a dairymaid, and a dairy is of course a place where the dey worked. But the Old English form of dey is dæge, and originally meant not a worker with milk, but a worker with bread - with dough, which is also related (Old English dáh).
So one problem is explaining how a known word dæge could have turned into a suffix díge. There might not be any known sound shift that can explain this, and you can't just hand-wave it away as some kind of random change. The Neogrammarian principle is very strong and very well tested in phonetics of languages we know this well. We need a reason for every change. That's why the fact that it looks like the root for knead isn't enough to justify saying that it unproblematically is.
Next is the meaning. Webster 1913 below us gives all the shades of meaning of 'lady' but the OED gives them in much greater detail, with dates against each. We think of the lady of a house being the wife. We think of your good lady, and the lady being the wife of the lord, and so on. But the original Old English idea was mistress, or ruler: the mistress of the household having power over servants, and the queen of an Anglo-Saxon kingdom, and the Virgin Mary. A lady was matched not with a gentleman or a husband, but with a lord. It is this exalted being who is considered relatively unlikely to soil her hands with dough. This is (presumably) why the OED contributors were reluctant to believe in the etymology.
From about 1200 the meaning spreads out, and it is then that the two common senses of 'wife' and 'high-born woman' arise. From about the time of Chaucer we get the chivalric sense of 'object of love, paramour, sweetheart'. But these extensions to what are now the familiar meanings of 'lady' shouldn't blind us to the fact that the original sense was narrower and less conducive to kneading dough.
The Old English root comes from a
Proto-Indo-European *dheigh-, which has several other interesting descendants. Its primary meaning is more abstractly that of moulding. It gives the Latin root
fig- which gives us
figure,
figment,
fiction, and
feign.
In Old Persian it gave a word daeza meaning 'wall'. Something walled around was pairi-daeza (cf. Greek peri-). The Greeks borrowed this word, in the form paradeisos, to describe the splendid walled gardens of the Persian kings, which is how ladies, dough, figures, and fictions are all connected to Paradise.