I say 'native speakers' because I think that this is a question of feeling for one's own language. I know that many dictionaries disagree with me.
ps. In my 'Reason for Editing (post #4) I think that 'listless' would be wrong.
I note that Raymott did not mention 'lackadaisical' when he wrote, "You used to be able to say 'fagged' or 'fagged out' for listless". Apart from that, there has not been the slightest indication that anybody else agrees with me, so I have to conclude that I have imagined a difference which does not in fact exist.
But, it's very hard to justify this or discuss this because lackadaisical is not a word any normal person would say, at least in my milieu. I don't think I've ever heard someone actually say this word in RL. And if they did, I'd think it was word-of-the-day on their calendar.
Lackadaisical carries a sense of unwillingness, lack of responsibility, so I wouldn't use it for grief.
(Sorry for unnecessary post- I hadn't seen the second page when I wrote it)