Lethe is one of the five rivers in Hades, the underworld in Greek mythology. Lethe means oblivion, forgetfulness or concealment (from Mythology.net). The River Lethe is the river of forgetfulness. The significance of the Greek river of forgetfulness appears to mirror Machado's own forgetfulness in her relationship. She continually "forgets" how deeply she is caught in the abusive relationship patterns with her partner. It seems as if, after each instance of abuse, she takes the hurt and pain in. She allows for each abusive instance to seep into her psyche and emotions.
This becomes interesting when it comes to the River Lethe allusion because one can argue that each time she allows the abuse to seep into her she is “drinking from Lethe” so to speak: “All those who drank from the river experienced forgetfulness, and Lethe’s murmuring sound would induce drowsiness” (from Mythology.net). As Machado forgets, her girlfriend grows drowsier and drowsier while driving. The two of them together are direct products of this Greek river. When Machado wakes her girlfriend up from nodding off while driving, the girlfriend is angry and in denial that she is sleepy. This is a sign of her own forgetfulness as well.
And let us not ignore the larger image of the two of them driving in darkness, at night, into oblivion, deeper into unconsciousness. Together, they are speeding into the daze, further into the stupor of their broken relationship.