In Chopin's The Awakening, the two lovers, as well as the woman in black, may provide symbolism and foreshadowing. (It is perhaps important to note that Chopin's stories present women who defy the social norm of the time, and were considered by some to be scandalous. This story ultimately ended Chopin's career as a writer.)
There is no doubt that Edna has reached a point where she is growing unhappy with a role in life that she does not feel she can identify with—wife to Léonce, and mother—and her husband sees this and (naturally) disapproves:
He reproached his wife with her inattention, her habitual neglect of the children. If it was not a mother's place to look after children, whose on earth was it?
This would, in part, explain her affair with Alcée Arobin. He is a player ("womanizer"): a man who has no problem becoming involved with a married woman—with any woman. It is a fling for both, for Edna would not leave her husband for Alcée, any more than he would offer her marriage. Neither is interested in a committed relationship, but neither loves the other.
However, this is a diversion for Edna who really loves Robert Lebrun. Robert is a man of character and depth. It is with Robert that Edna can have meaningful discussions, see the town, and meet unusual residents of the island—in other words, Edna is introduced to a new and enticing world.
...she was seeing with different eyes and making the acquaintance of new conditions in herself that colored and changed her environment, she did not yet suspect.
In these daily sojourns with Robert, Edna falls in love. Robert fights his desire to form an intimate relationship with Edna because he believes that it is wrong. He wants no part in breaking up Edna's marriage. However, once Edna has seen this other world, and the more she realizes that she will never have Robert, she chooses death to the life she knew before.
This is a theme similar to that of Chopin's "The Story of an Hour," where the protagonist experiences an awakening to freedom she has never known. When she loses that sense of liberation, she is so bereft that she has a heart attack. The loss she experiences in face of her recent awakening and the knowledge that she will be a prisoner for the remainder of her life is more than her heart can stand.
Here, too, Edna cannot face a life without freedom; she cannot conceive of living without Robert and all he stands for. Edna chooses to die: she goes down to the ocean and walks in, taking her life.
The lovers symbolize Edna's desire to have a complete relationship with Robert: not just with discussions, but a physical joining as well as an emotional one. The woman in black could well symbolize death itself. (Also a woman in that era dressed in black was most likely in mourning: dressed to show respect for the loss of someone closely related.) She could also symbolize Edna's loss of affection for her husband, or the end of Edna's marriage in her heart.
Putting these characters together, we can suggest that the presence of the lovers and the woman in black foreshadow the story's end. For unable to have the life she wants (as Robert's lover), Edna commits suicide rather than return to a life that no longer has meaning for her. (Death is represented by the woman in black.)
I would give up the unessential; I would give my money, I would give my life for my children; but I wouldn't give myself.