There are certain parts of the Scripture that have made their way into the public consciousness even among those who do not care for the Word of God. The Good Samaritan, David and Goliath, even Samson and Delilah show up in commercials, movies, politics, and more...but I don't know that any of those match Sodom and Gomorrah. After all, it has only been the last few decades that "sodomy" laws have been stricken from the books in this country.
That's a pretty long recollection, and a pretty infamous one. Why would our memory of Sodom and Gomorrah be so long and so angry? A few reasons. First of all, you probably noticed that Genesis 18 ended with Abraham speaking with God about sparing these cities from destruction.
After all, a gracious God wouldn't destroy the righteous with the wicked (Genesis 18:25), right? Yet after going so far as to say that He would not destroy the cities if 10 righteous men could be found there...Sodom and Gomorrah are destroyed. And it's not that God didn't look hard enough.
The story opens like some tales we find in ancient mythology, where the gods come down in disguise to test humanity. Usually, the stories survive where only a handful pass the test.(See Bacchus and Philemon (not Bible Philemon) as an example, also note The Iliad and The Odyssey for some discussion). Given the antiquity of the events of Sodom and Gomorrah, however, this could be the event behind the evolved legendary tales.
Either way, God's messengers come to Sodom and are offered hospitality only by Lot. Here he is a foreigner, but the only one who fulfills the expectations of hospitality. And, by extension, the only one who stands between Sodom and Gomorrah...and judgment.
And as a practical matter: 1) Christians, if you are the one righteous family in town, perhaps your behavior in a righteous manner is part of how God shows grace to your town. You could be the one that God uses. 2) It would be pretty terrible to be a resident of a place that is so sure of its own righteousness that only the foreigners and outsiders get life right.
The angels come, Lot provides them with hospitality, and then things go very wrong. The men of the city, pretty much all of them, come and demand the angels be given over for sexual purposes. There's a lot left unsaid here, though a question I still have is this: Do they do this to every new person in town? If so, what about Lot?
Note that the angels are not clearly angels to the people, so there is no weird lust for the supernatural beings. Instead, it is a desire for power through sexual dominance. We see how far Lot has fallen, that he offers the crowd the freedom to abuse his daughters in place of the men. And, no, "hospitality" is no excuse for this: it would be one thing for Lot to have armed himself and his sons (if had any) and they all died fighting to protect the angels.
But sacrificing his daughters to the crowd's lust? This is not a righteous, excusable action under any circumstances.
After seeing the lust of the crowd and their fervor for unrighteousness--no matter your view on human sexuality, even if it departs from the Biblical ethic, I doubt anyone finds forced sexual activity righteous--then the angels pull Lot and his family out. We see how weak Lot's influence is when his own sons-in-law (marriage processes were different, they were not yet married to his daughters but still defined as this relationship) refuse his summons to escape. His wife looks back, longingly, for the life they had in the wicked places...and is lost.
Ultimately, the two biggest trouble-making nations for Israel, Moab and Ammon, have their origin here. Lot's daughters turn their father's earlier offer on its head, and use him for their needs. The drunken incest brings about the Moabites and Ammonites, two nations that fight Israel for many centuries. And, it may be noted, worship terrible idols.
The long and short of it is this: Lot may have been related to Abraham, but he never grabbed hold of Abraham's relationship with God. There is no long-term "once removed" relationship with God: every one must follow God themselves.