A lai is a poem to be sung, detailing an adventure or a romance. The oldest known lais were written by Marie de France in the tweflth century court of Henry II. Verses are written with eight syllables, and often detail a narrative of King Arthur and other Celtic heroes. Provence's lyric love songs were also known as lais.
Zooming forward to the fourteenth century of England, comprable poetry was composed under the name of Breton lays--the most well-known example being Geoffrey Chaucer's The Franklin's Tale. Since then, historical ballads are often still called lays.
NTC's Dictionary of Literary Terms by Morner & Rausch