1590s, "bright, shining" (a sense now obsolete or restricted), from Latin lucidus "light, bright, clear," figuratively "perspicuous, lucid, clear," from lucere "to shine," from lux (genitive lucis) "light," from PIE root *leuk- "to shine, be bright."
Sense of "easy to understand, free from obscurity of meaning, marked by intellectual clarity" first recorded 1786. Lucid interval "period of calm or temporary sanity" (1580s) is from Medieval Latin lucida intervalla (plural), common in medieval legal documents (non est compos mentis, sed gaudet lucidis intervallis, etc.). The notion probably is of a period of calm and clear during a storm. Related: Lucidly; lucidness (1640s).