From the clues we have so far, Kononotsu seem to be for a beautiful girl who can dance.
It was for a ritual of some sort? If God and liar are the same person, then. It means this liar want to make a ritual by using a perfect girl to get something that he couldn't do it by himself.
Of course, he might not be a god at all. But, it's just a guy who claimed to be. Even Those Kokonotsu might come from someone else.
The tale might be twisted from time to time. So, the thing that they heard might be not true at all.