c. 1200, lafdi, lavede, from Old English hlæfdige (Northumbrian hlafdia, Mercian hlafdie), "mistress of a household, wife of a lord," apparently literally "one who kneads bread," from hlaf "bread" (see loaf (n.)) + -dige "maid," which is related to dæge "maker of dough" (which is the first element in dairy; see dey (n.1)). Also compare lord (n.)). Century Dictionary finds this etymology "improbable," and OED rates it "not very plausible with regard to sense," but no one seems to have a better explanation.
The medial -f- disappeared 14c. The word is not found outside English except where borrowed from it. Sense of "woman of superior position in society" is c. 1200; that of "woman whose manners and sensibilities befit her for high rank in society" is from 1861 (ladylike suggesting this sense is attested from 1580s, and ladily from c. 1400). Meaning "woman chosen as an object of chivalrous love" is from early 14c. Used commonly as an address to any woman since 1890s.
Applied since Old English to the Holy Virgin, hence many extended usages in plant names, place names, etc., from genitive singular hlæfdigan, which in Middle English merged with the nominative, so that lady- often represents (Our) Lady's, as in ladybug. Lady Day (late 13c.) was the festival of the Annunciation of the Virgin Mary (March 25). Ladies' man first recorded 1784; lady-killer "man supposed to be dangerously fascinating to women" is from 1811. Lady of pleasure recorded from 1640s. Lady's slipper as a type of orchid is from 1590s.
Old English dæge "female servant, woman who handles food in a household, housekeeper," from Proto-Germanic *daigjon (source also of Old Norse deigja "maid, female servant," Swedish deja "dairymaid"), from PIE root *dheigh- "to form, build." Now obsolete (though OED says, "Still in living use in parts of Scotland"), it forms the first element of dairy and the second of lady.
OED says the ground sense of the ancient word seems to be "kneader, maker of bread;" it would have then advanced via Old Norse deigja and Middle English daie to mean "female servant, woman employed in a house or on a farm." By c. 1200 it had acquired the specific sense of "woman in charge of milking and making butter and cheese, dairy-maid." Dæge as "servant" is the second element in many surnames ending in -day (such as Faraday, and perhaps Doubleday, if it means "servant of the Twin," etc.).