c. 1400, "loose" (in reference to bowels), from Latin laxus "wide, spacious, roomy," figuratively "loose, free, wide" (also used of indulgent rule and low prices), from PIE *lag-so-, suffixed form of root *sleg- "be slack, be languid."
In English, of rules, discipline, etc., from mid-15c. Related: Laxly; laxness. A transposed Vulgar Latin form yielded Old French lasche, French lâche. The laxists, though they formed no avowed school, were nonetheless condemned by Innocent XI in 1679.