Pope's "The Rape of the Lock" is a mock-epic, meaning that it is written in the style of an ancient epic poem but that the events it contains are utterly trivial. The entire poem is based around one such event, the illicit cutting of a society lady's hair by one of her suitors.
By most people's standards, this wouldn't be much to get excited about. But to the upper-class worthies of eighteenth-century English high society, it's a pretty big deal, on a par with the Trojan War depicted by Homer in the Iliad.
It can reasonably be said, then, that "The Rape of the Lock" is an extended metaphor, a comparison of two completely different things that nonetheless have something in common. In this particular case, what is common between ancient Greek society and that of eighteenth-century England is a firm belief in the importance of maintaining one's honor.
In the Iliad, the Achaeans go to war with the Trojans because the honor of King Menelaus has been violated by his wife's running off to Troy to be with Paris. And in "The Rape of the Lock," Belinda embarks upon an epic quest to get back the lock of hair stolen from her by the Baron. She, too, feels that her honor has been violated.
On a superficial level, then, there is a comparison to be made between the action of the Iliad and "The Rape of the Lock." But on a much deeper level, there's a huge difference between what the protagonists of these poems are fighting for.
The Trojans and Achaeans are engaged in a long, drawn-out conflict that will eventually result in the destruction of the city of Troy. Belinda, on the other hand, is simply trying to get a piece of her hair back. And whereas the combatants in the Trojan War fight on the blood-drenched field of battle in vicious hand-to-hand combat, in "The Rape of the Lock," we have a battle of the teacups, during which the Baron sneezes the lock of Belinda's hair high into the air.
Belinda's attempts to get her hair back may very well constitute a quest; they may even constitute an epic quest; but in the event, Belinda's making an almighty mountain out of the tiniest of molehills. Not even the presence of figures from Greek mythology, such as sylphs, or the numerous elements from ancient epic can change that simple fact.