early 14c., sodaine, from Anglo-French sodein or directly from Old French sodain, subdain "immediate, sudden" (Modern French soudain), from Vulgar Latin *subitanus, variant of Latin subitaneus "sudden," from subitus past participle of subire "go under; occur secretly, come or go up stealthily," from sub "up to" (see sub-) + ire "come, go" (from PIE root *ei- "to go"). "The present spelling was not finally established till after 1700" [OED].
Noun meaning "that which is sudden, a sudden need or emergency" is from 1550s, obsolete except in phrase all of a sudden first attested 1680s, also of a sudayn (1590s), upon the soden (1550s). Sudden death, tie-breakers in sports, first recorded 1927; earlier in reference to coin tosses (1834). Related: Suddenness.
-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.