Lily seems to spend an unhealthy amount of time poised on the edge of some type of cliff, ready to fall down into some sort of metaphorical abyss. The first mention of said chasm arises when Lily debates whether or not to purchase the blackmail letters from the charwoman:
If she weighed all these things it was unconsciously: she was aware only of feeling that Selden would wish the letters rescued, and that therefore she must obtain possession of them. Beyond that her mind did not travel. She had, indeed, a quick vision of returning the packet to Bertha Dorset, and of the opportunities the restitution offered; but this thought lit up abysses from which she shrank back ashamed.
It's should be no surprise to you by now that, like everything else in House of Mirth, this abyss has something to do with morality. Lily feels that the gaping darkness below her is the darkness of moral destitution. Now, let's look at Abyss #2, when Selden encounters Lily in Monte Carlo before the Dorset scandal has taken place:
[Lily] was on the edge of something – that was the impression left with him. He seemed to see her poised on the brink of a chasm, with one graceful foot advanced to assert her unconsciousness that the ground was failing her.
Lily is indeed about to take a fall – a fall which will be moral in the eyes of those around her (who believe she has engaged in an affair with George Dorset), social, and also financial. Much of Book II is composed of Lily's great fall from grace, from a member of the social elite to a destitute member of the working class. But we can't wrap this discussion up yet; the idea of the abyss comes back into play right at the end of the novel, when Lily muses on her encounter with Nettie Struther:
The poor little working-girl who had found strength to gather up the fragments of her life, and build herself a shelter with them, seemed to Lily to have reached the central truth of existence. It was a meager enough life, on the grim edge of poverty, with scant margin for possibilities of sickness or mischance, but it had the frail audacious permanence of a bird's nest built on the edge of a cliff – a mere wisp of leaves and straw, yet so put together that the lives entrusted to it may hang safely over the abyss.
Nettie is on the edge of the abyss of poverty and insignificance. (Remember how Lily is just as concerned with isolation and meaninglessness as she is with finances in the moments before her death?) Yet Nettie is safe, Lily concludes, because she has both permanence and love in her home and in her husband. Poverty doesn't threaten Nettie the way it does Lily. For our heroine, though, the abyss still yawns before her and, by the end of the novel, seems to represent all that has plagued Lily throughout the novel: poverty, moral ruin, and even death, as we see in this last passage:
The very slowness and hesitancy of the effect increased its fascination: it was delicious to lean over and look down into the dim abysses of unconsciousness.
Unconsciousness might mean sleep, but it also refers to death. Which one Lily is seeking at this point is, as always, up to you to decide.