A Few Notes on the Play:
First, let me explain the location, the House of Hades. The House of Hades, the Greek version of the underworld, contained five rivers, the Styx, the Lethe, the Acheron, the Cocytus, and the Phlegethon. The Lethe, which was mentioned in the play, was the river of forgetfulness. According to mythology, the dead would drink from this river in order to forget their past life, so they would not retain their memories into their next reincarnation. It is by this river we find Agamemnon, who is summarizing the events that lead up to his death. Iphigenia, who has been waiting for him, starts to greet him, but catches herself. She remembers that she was sacrificed, and becomes hesitant. She is unsure if her father still loves her, since he sent her to die, and she has spent the years in the underworld since her death contemplating her sacrifice, and whether or not it was necessary. She is also angry with her father for lying to her mother and her siblings, since she knows it only made her death harder for them to bear. She also asks her father to re-explain her sacrifice. Agamemnon defends himself, saying that he had no choice to sacrifice her, that she would have died anyway, and appeals to her love of her family, telling her that if she had not been sacrificed, everyone else would have died with her. However, this time, Iphigenia has had years to consider the situation, and reminds him that he was the one who angered Artemis; When he made the choice to kill her rabbits, he also made the choice to kill her as well. (I admit Iphigenia's line there was voicing my own judgment of Agamemnon, mainly because I disliked that his daughter had to die for his own mistake, and his own greed.)
Iphigenia turns to leave, but her father, who has spent the Trojan War stewing in his regret over his daughter's death, begs her not to go. Iphigenia hesitates when she hears her father's plea, because it is an unusual tone for his voice to take. Agamemnon usually demands what he wants, instead of asking. She stops, but asks him if he noticed the wind that came before the execution, although it was her death that was supposed to release the wind. When Agamemnon replies that he did notice, and then tried to stop the sacrifice, she forgives him somewhat. She allows him to embrace her, even if she does not return it.
Since the matter of her sacrifice has been cleared up, she then asks her father why he is dead. Her father, figuring that being sacrificed on her supposed "wedding day" was traumatic enough, lies to her and tells her that he perished in battle, instead of revealing that her mother, Clytemnestra, murdered him upon his return over Iphigenia's death. They then go to drink from the Lethe, in order to forget the circumstances of their deaths and to start over in a new life.