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.
"salmon," from Old English leax (see lox). Cognate with Middle Dutch lacks, German Lachs, Danish laks, etc.; according to OED the English word was obsolete except in the north and Scotland from 17c., reintroduced in reference to Scottish or Norwegian salmon.