c. 1300, seculer, in reference to clergy, “living in the world, not belonging to a religious order,” also generally, “belonging to the state” (as opposed to the Church), from Old French seculer, seculare (Modern French séculier) and directly from Late Latin saecularis “worldly, secular, pertaining to a generation or age,” in classical Latin “of or belonging to an age, occurring once in an age,” from saeculum “age, span of time, lifetime, generation, breed.” …

The ancient Roman ludi saeculares was a three-day, day-and-night celebration coming once in an “age” (120 years). Ecclesiastical writers in Latin used it as those in Greek did aiōn “of this world” (see cosmos). It is the source of French siècle “century.” The meaning “of or belonging to an age or a long period,” especially occurring once in a century, was in English from 1590s.

https://www.etymonline.com/word/secular

Generation is commonly used in the sense of a fairly short span of time, ~20 years. Secular cycle, googling quickly, seems to be using secular more in the ‘lifetime/age’ sense since the cycles are over the course of a couple centuries.