Hi,
There is no love lost between them." means "they are at odds." but I'd like to know what the etymology of the idiom is. It seems to mean the opposite thing without the knowledge of what it really means.
I don't see it as a matter of etymology. I think it's a question of understanding the meaning clearly.
They dislike each other absolutely, completely.
Any love, even a tiny amount, that was between them would be wasted, ie 'lost'. But there is not even a tiny amount of love between them, so 'there is no love wasted (ie lost) between them'.
Best wishes, Clive