Why does the Torah find it necessary to mention that Lot was Avraham's nephew?
Seforno: The four kings made a special effort to capture Lot, precisely because he was Avraham's nephew, and they assumed that Avraham, who was extremely wealthy, would pay a handsome price for his release.
Chachmah u'Musar (2 p.370): Also "they took" and "he dwells in Sedom" are extra. This is unlike nature, that they should be able to capture Avraham's nephew, whom Avraham taught and trained. What caused this? He dwelled in Sedom.
And why does it see fit to remind us that he lived in Sedom?
Rashi: To tell us that Lot had only himself to blame for his capture, because he chose to live in Sedom.
רש"י: מי גרם לו...ישיבתו בסדום: מנין לדרוש כך?
גור אריה: אם לא כן, פסוק זה מיותר, כי כבר כתוב לעיל שישב בסדום.