According to the Oxford Dictionary of English, on my Kindle App, lackadaisical means “lacking enthusiasm and determination; carelessly lazy”. The OED gives this example: “a lackadaisical defence left Spurs adrift in the second half”. The same source defines the word lax as “not sufficiently strict, severe, or careful”. There is no such word as “laxadaisical”, though that doesn’t stop people from using it. I recently heard a pundit on “Match of the Day” describe a player as “a bit lacksy-daisy”. “Lacksy-daisy” is not a proper word either.
My brother and his business partner, at the Language School they run in Spain, are very precise about the words they use. They know well enough not to correct each other’s grammar, pronunciation or choice of words. Some years ago my brother’s business partner told him that she had just learnt that “laxadaisical” wasn’t a word. It’s “lackadaisical”. Did he know? Yes, he told her. (He had noticed when she used the incorrect form, but knew better than to correct her about it.) He also knew the derivation, from the archaic term “lackaday”, used by people who believed the end of the world was nigh. Or, as this quote from dailywritingtips.com puts it:
The adjective lackadaisical derives ultimately from the word lack in the Middle English sense of “loss, failure, reproach, shame.” When people were overcome by the sadness, unfairness, or futility of life, they would put the back of their hands to their foreheads and exclaim “Ah, lack!”
“Ah, lack” became the word alack. Then came the expression “Alack the day!”
Feeling “overcome by the sadness, unfairness, or futility of life”? That might make you feel rather lackadaisical, and you might not even care that “laxadaisical” isn’t a real word.