c. 1200, "solemn prayer of supplication," from Old French letanie (13c., Modern French litanie) and directly from Medieval Latin letania, Late Latin litania (source also of Spanish letania, Italian litania), from Greek litaneia "prayer, an entreating," from lite "prayer, supplication, entreaty," a word of unknown origin. From the notion of monotonous enumeration of petitions in Christian prayer services came the generalized sense of "repeated series" (early 19c.), which originated in French.
For those who know the Greek words, a litany is a series of prayers, a liturgy is a canon of public service; the latter in practice includes prayer, but does not say so. [Fowler]