If two people love each other, then fall out (because of an argument or other reason), then there was love lost between them. But if two people don't care much for each other, then have a falling out, then there really was no love lost between them.
Interestingly, when it was originated in the 1500s, until about 1800, it could indicate either extreme love or extreme hate.
Extreme love (the image is of love shared in a common vessel; when affection was mutual, none of the love in the vessel was lost):
- Sore sicke he was, and like to dye,
No helpe his life could save;
His wife by him as sicke did lye,
And both possest one grave.
No love between these two was lost,
Each was to other kinde;
In love they liv'd, in love they dyed,
And left two babes behinde." - Reliques of Ancient English Poetry, 1765
You can tell it's from some time ago; the two innocent children die in the woods!
Here, Manville, a gentleman, loves a peasants daughter, Em. Em speaks of him:
- And never could I see a man, methought,
That equaled Manville in my partial eye.
Nor was there any love between us lost,
But that I held the same in high regard, . - Faire Em, (a fraudulent Shakespeare) - Act V, Sc. I (1592)
"There's no love lost," quote Sancho, "for she speaks ill of me too when she list." - Don Quixote. 1620 translation
Today, however, the term signifies ill will exclusively. If there is no love lost between two people, they have a strong enmity towards or hate for the other and make no effort to conceal it.
He needs her appearance of moral integrity, and she needs his iron to end all argument about her unity and purity. It is a marriage of convenience, a strained relationship, with no love lost between them. For both, the hope of world dominion is worth the tension.