What is the moral lesson of the myth about Persephone?

As with most of the Greek myths, the overriding moral is not to defy the gods. The gods are presented not as moral exemplars but as capricious and amoral tyrants, shamelessly using mortals to get what they want, whenever they want it. Yet however badly the gods behave, the divine will must always be obeyed, otherwise there will be serious consequences.
In the myth of Persephone, Demeter does what any normal mother would do in a similar circumstance and searches high and low for her abducted daughter. But Demeter is also a goddess, and as such she has no hesitation in wreaking revenge upon the mortal world, which she holds responsible for Persephone's disappearance.
Unknown to Demeter, however, her daughter has been abducted by Hades and spirited away to his underworld domain. Not only that, but this was all part of a plan cooked up between the god of the underworld and the mighty Zeus himself. As the father of the gods has so decreed that Persephone must yield to Hades, there is nothing that Demeter can do about it. Persephone has learned the hard way that the will of Zeus must always be obeyed, irrespective of the terrible consequences that sometimes follow. Bearing in mind also that Zeus is Persephone's father, we might also see the myth as reinforcing existing gender relations in ancient Greek society, where men were expected to exercise complete control over their wives and daughters.

Persephone is the daughter of Zeus and the harvest god Demeter. In the classic mythological story, she is following along with her mother Demeter one day and is abducted by Hades, the god of the underworld. Demeter is furious and by withholding her life-giving powers to bring vegetation to the earth, she forces Zeus to confront Hades and secure Persephone's return. Hades tricks Persephone by giving her pomegranate seeds to eat, and because of this, she is forced thereafter to spend a portion of every year down in the underworld with him.
This myth becomes an sort of moral story or explanation for the change of seasons. When Persephone and her mother Demeter are reunited, the earth springs forth with life. But when she is forced to return to the underworld for a time every year, the earth once again becomes more lifeless and barren.
The myth is repeated in many different contexts and is adopted by the Roman tradition as well, with Demeter being replaced by Ceres, Zeus by Jupiter and Hades by Pluto.
https://www.theguardian.com/books/2008/jan/12/greekmyths.greekmythsfeatures3