"impudently, with impertinent boldness," 1540s; see saucy + -ly (2).
Entries linking to saucily
saucy adj.
c. 1500, "resembling sauce" (a sense now obsolete), later, of persons, words, etc., "impertinent in speech or conduct, flippantly bold, cheeky" (1520s), from sauce (n.) + -y (2). The connecting notion is sauce in the figurative sense of "that which adds intensity, piquancy in words or actions."
Compare Skelton's have eaten sauce for "be abusive." Also compare sauce malapert "impertinence" (1520s), and sauce (n.) in its obsolete use as a vocative for "impudent person" (1530s). In Shakespeare, with overtones of "wanton, lascivious," it was "a term of serious condemnation" [OED]. Also compare salty in similar senses.
-ly 2
common adverbial suffix, forming from adjectives adverbs signifying "in a manner denoted by" the adjective, Middle English, from Old English -lice, from Proto-Germanic *-liko- (cognates: Old Frisian -like, Old Saxon -liko, Dutch -lijk, Old High German -licho, German -lich, Old Norse -liga, Gothic -leiko); see -ly (1). Cognate with lich, and identical with like (adj.).
Weekley notes as "curious" that Germanic uses a word essentially meaning "body" for the adverbial formation, while Romanic uses one meaning "mind" (as in French constamment from Latin constanti mente). The modern English form emerged in late Middle English, probably from influence of Old Norse -liga.