Genesis 18:1 to 22:24, 2 Kings 4:1-37
The angels cannot destroy S'dom and Amorah until Lot departs (19:22), but spare Lot and his three family members only for the sake of Avraham's prayer (19:29). This implies Lot's future descendants were considered by God as part of the "ten or more" righteous in S'dom.
After the Akedah, God does not extend the covenant with Avraham but instead swears an oath (22:16-18)
Rabbi Levi Yitzchak taught:
Do you know the difference between our Father Avraham, peace be with him, and his nephew Lot? Why does such a spirit of satisfaction pervade the story of how Avraham lset before the angels curd and milk and tender calf? Did not Lot also bake for them and give them food? In Lot's case it is written that angels came to Sodom. But concerning Avraham, scripture says: "...and he looked up and saw three men standing opposite him." Lot saw angelic shapes; Avraham saw poor, dusty wayfarers in need of food and rest.
This parasha begins "God appeared to him..." without saying Avraham's name to emphasize that these events are connected with what happened previously. God himself is performing the mitzvah of visiting the sick, for Avraham is weak after circumcizing himself.
The three men (angels) were both "standing by him" and far enough away that he ran to meet them (verses 18:1-2). The first phrase means they appeared suddenly from nowhere, but Avraham did not see this.
In verse 18:3 Avraham speaks only to one of the men ("my lord" and "your (servant)" are grammaticaly both in the singular); Avraham only requests a decision about plans from the apparent senior. In verse 18:4 Avraham speaks to all the men, to make clear he will be hospitable to all of them.
R' Elazar notes that Avraham only promises bread and water, but prepares a feast of cakes (of fine flour, not inferior "meal"), butter, milk, and meat. But R' Bechaye wrutes that cakes were not actually served because the dough was observed to be impure.
The word zakayn (old) first occurs in verse 18:12. There is a traditional story that until Avraham people lacked visible signs of aging. Avraham asked God, "How shall we know when to show proper respect to the elderly?"; God answered, "You speak well and from your time on I will do this," and made Avraham's hair grey.
The first "white lie" of scripture occurs in verse 18:13, when God speaks as if Sarah had called herself old instead of what actually happened -- she had called Avraham too old.
Sarah laughs b'keerbah (within herself) yet God hears her. Sarah then claims that did not count as laughing, but God says unvoiced doubt still counts.
Tradition ascribes to different "primary sins" to S'dom and Amorah, both linked to their location in the most fertile part of the land. Some stories claim their significant crime was their refusal to give charity. Other stories claim it is a custom of abusing visitors so that outsiders would not desire to move to their prime land.
When the flood happened, the righteous were Noach, his wife, his three children, and their three wives. This makes eight people. Since Avraham knew the entire world was not spared for eight righteous people, he did not ask if two mere cities would be spared for less than ten people.
Alternately, perhaps Lot's married "sons" were three in number. Then Lot, his wife, his two unmarried daughters, his three sons, and his three daughters-in-law would total the ten people that Avraham was counting on to save S'dom and Amorah.
R' Bechaye and the author of Toldos Yitzchak write that Lot did not run to meet the angels since it was dark and he did not see them until they were near. Lot also prepared a feast and bread, but he prepared unleavened bread instead of cakes of fine flour.
Rashi writes that the town of Tzoar was newly built, still small, and thus had not committed many sins; it was called Bela previously (14:2). But notice Lot pleads only for his own ease and safety, whereas Avraham pleaded that God acts righteously. Why does Lot leave Tzoar promptly? Because he was afraid it also would be judged and destroyed.
Verse 19:23 implies the sun and moon were both still visible. This is so that both the sun-worshippers and moon-worshippers in S'dom and Amorah would realize their supposed diety was watching but failed to save them.
Lot's elder daughter flaunted her sin. The text says of her "she lay with her father" and she names the child Moav which means "from a father". The younger daughter was discrete. The text only says "she lay with him" and her child is called Ben-Ami which means "son of my nation". Neither would have sinned had they understood that (unlike with the flood) the entire world was not destroyed. Since the younger daughter was ashamed when she believed she had to necessarily sin, God protects the nation of Ammon.
Why did Avraham leave Mamre? Avraham valued showing hospitality, and with the nearby towns destroyed he someplace else so he would have visitors.
In verse 20:11 Avraham does not imply Avimelech is wicked, but that others in his city of Gerar might be wicked. Avimelech, unlike the Pharaoh of chapter 13, allows Avraham to stay in his territory.
According to one tradition, Yishmael mocked Yitzchak in verse 21:9 by saying, "You may have a feast in your honor today, but I am the eldest son and will have double your inheritance." This is why Sarah was thinking of inheritance in the next verse. Alternately, Yishmael had no inheritance as the son of a slave, and was simply teasing Yitzchak; Sarah's use of the word yarash should not be translated as "shall not be heir with my son" but rather "shall not dominate the home he shares my son".
Hagar had given up on Yishmael: she "threw" (tashlaych) him under the tree instead of placing him there, and was crying instead of praying. This is why God responded to Yishmael's cries but not Hagar's.
God never told Avraham to kill Yitzchak. The command was V'ha'alayhoo sham l'olah ("make him rise there as an offering"). God only desired that Avraham symbolically offer Yitzchak by binding him on an altar. This is why this episode is called the Akedah ("binding"). But Avraham misunderstood and believed he was supposed to kill Yitzchak.
Tradition includes stories of Satan appearing to Avraham, Yitzchak, and Sarah during the the Akedah, trying to turn them from obedience. The stories are similar to Yeshua's accounts of how Satan tempted him in the wilderness.
Chapter 22 ends with Avraham hearing of the birth of Rivkah, who will eventually become Yitzchak's wife. This is because Avraham was tempted, after the Akedah, to marry Yitzchak quickly to most speedily see happen the promise of descendants through Yitzchak. But God was warning Avraham to wait for the right bride.