Yes, more mythology. Here's the back-story: the furies were mythical creatures in ancient Greece who embodied vengeance. Basically, if you did something wrong, these scary, winged creatures would hunt after you for the rest of your life. The go-to ancient text here is a tragic play by the Greek playwright Aeschylus, called Eumenides. In it, a man named Orestes is relentlessly pursued by the furies as punishment. "Eumenides" means "friendly ones" and was a euphemism used to refer to the furies.
What does this have to do with House of Mirth? Take a look:
[Lily] had once picked up, in a house where she was staying, a translation of the Eumenides, and her imagination had been seized by the high terror of the scene where Orestes, in the cave of the oracle, finds his implacable huntresses asleep, and snatches an hour's repose. Yes, the Furies might sometimes sleep, but they were there, always there in the dark corners, and now they were awake and the iron clang of their wings was in her brain . . . (1.13.78)
This is Lily's reaction after she flees Trenor's house late at night and finds herself compromised and in despair. Later that night, she says: "Oh, Gerty, the furies…you know the noise of their wings – alone, at night, in the dark? But you don't know – there is nothing to make the dark dreadful to you" (1.14.78). Lily clearly identifies herself with Orestes, but what are the furies to her? What is it that she feels relentlessly pursuing her throughout the course of the novel? To answer this, let's look at some more references to the furies.
[The next morning:] In the solitude of her own room she was brought back to a sharp contemplation of facts. Her daylight view of them necessarily differed from the cloudy vision of the night. The winged furies were now prowling gossips who dropped in on each other for tea. But her fears seemed the uglier, thus shorn of their vagueness; and besides, she had to act, not rave. For the first time she forced herself to reckon up the exact amount of her debt to Trenor. (1.15.12)
[After Mrs. Peniston refuses to help with her debt:] Lily went up to her own room and bolted the door. She was trembling with fear and anger – the rush of the furies' wings was in her ears. She walked up and down the room with blind irregular steps. The last door of escape was closed – she felt herself shut in with her dishonour. (1.15.48)
Lily has identified the furies as the sense of obligation she feels to pay Trenor back his nine thousand dollars. That's why the sound of the wings abates when she has hope of getting the money from her aunt, and comes back with a fury when Mrs. Peniston refuses to help. Running away from New York to Europe means Lily is actually taking the same course of action that Orestes did – trying to flee the furies. Does it work? That would be a "no." Lily returns to New York to find that, sadly, her debt didn't magically disappear while she was gone. She assumes the obligation to pay it back once more, but we don't hear about the furies again until close to the end of the novel, when Selden offers Lily a quick-fix out of debt:
She was quite sure that [Selden] would come and see her again, and almost sure that, if he did, she could bring him to the point of offering to marry her on the terms she had previously rejected. Would she still reject them if they were offered? More and more, with every fresh mischance befalling her, did the pursuing furies seem to take the shape of Bertha Dorset; and close at hand, safely locked among her papers, lay the means of ending their pursuit. The temptation, which her scorn of Rosedale had once enabled her to reject, now insistently returned upon her; and how much strength was left her to oppose it? (2.10.96)
Now that Lily has grown into a moral woman concerned with scruples instead of cash, the furies no longer take the shape of her financial concern; they take the shape of a moral one. She's no longer concerned about having to pay back her debt; she's concerned that she will cop out, use the letters, and marry Rosedale for the quick-fix. As Lily's perceptions and attitude have changed, so have changed the novel's symbols and the ideas they represent.