During the days between Christmas and New Year things may seem a bit more lax than usual, so I thought I’d look into the origins of the word.
Lax means lenient and allowing for deviation, not strict, loose, not tight or taut, lacking care, neglectful or negligent. It comes from the Latin laxus (wide, roomy, loose), from Proto-Indo-European *slǵ-so (weak, faint) [source].
The English word leash comes from the same roots, via the Middle English lesse (a leash for holding a coursing hound or watchdog) [source], the Old French lesse (leash, lead), and the Latin laxā (thong, a loose cord), from laxus [source].
The English word lease also comes from the same roots, at least partly: from Middle English *lesen, the Anglo-Norman lesser/lasier (to let, let go), from Latin laxō (to loose) from laxus, and partly from Old High German lāzan (to let, let go, release) [source].
Related words in other languages include laks (lax, slack) in Dutch, lâche (loose, slack, coward(ly), low, lazy) in French, lax (lax, easy, loose) in Geman, and llaes (loose, slack, free, trailing, flowing, low) in Welsh [source].
In Swedish, “lax” means salmon (the fish Salmo salar).
In Acadian and/or Cajun French, the word “lâche” is heard in the phrase “Lâche pas la patate” which means something like “Don’t give up”.