“Alack!” originally meant something like “Alas!” It bore connotations of dissatisfaction or shame. “Alack the day!” meant at first “may the day be shamed in which this awful thing has happened.” Later, it came to be abbreviated “lack-a-day” and used to express mere surprise.
The expression was gradually weakened, shifting from expressions of anguish to resigned despair, to languid indifference. The end result is the modern form “lackadaisical,” which conveys a lack of enthusiasm—a casual, perfunctory way of doing things.
This final meaning suggests “laxness” to some people who then misspell the word “laxadaisical,” but this is nonstandard.