Lot, Avram, and Sarai were travel partners even before the beginning of Parashat Lekh Lekha. See Genesis 11:31.
When God tells Avram to leave his homeland and his family, he takes Lot with him.
Professor Nechama Leibowitz, one of the greatest Torah scholars and educators of the twentieth century, thought that a significant change occurs between Chapter 12 and Chapter 13. Note how Lot is described in Chapter 13 and how it is different than how Lot was described in Chapter 12.
A few verses later and the Torah is describing conflict between Avram and Lot.
Based on all that you have seen:
1. Was it right for Avram to bring Lot with him?
2. What was the source for Avram and Lot becoming more distant?
3. What was the nature of the conflict described in Gen. 13:7?
See the selected comment of Ramban (Rabbi Moshe ben Nachman, d. 1263) to Genesis 13:7. What does Ramban believe was the cause of the conflict? If you like you can find a longer selection of Ramban in the Rubin Edition of Mikra'ot Gedolot.
ועל דרך הפשט היתה המריבה על המרעה כי לא נשא אותם הארץ וכאשר היה מקנה אברם רועה באחו היו רועי לוט באים בגבולם ורועים שם
The plain meaning of the narrative implies that the quarrel was over the cattle, since the land could not bear them and when Abraham's cattle were feeding in the meadow, Lot's shepherds would come along and feed there.
The Midrash presents a different, less pragmatic, foundation for the dispute between Avraham and Lot. How would you characterize this dispute?
Rabbi Berachiah in the name of Rabbi Yehudah ben Rabbi Simon said: the best of our father Avraham used to go out with a muzzle and Lot's animal had no muzzle. Avraham's shepherds used to say "are you allowed to commit robbery?" And Lot's shepherds would respond, "The Holy Blessed One said to Avraham that this land will be given to your children. Avraham cannot have children of his own. Soon he will die and Lot will inherit him so that even if the cattle are eating in the pastures that belong to others it is ultimately our own property that the cattle are eating."
According to the Midrash, Lot and Avraham had an irreconcilable conflict of values. Can you identify Lot's priorities and Avram's priorities? When Avram and Lot separate, how does Lot choose a new place to live?
Rashi (Rabbi Shlomo Yitzchaki 1040-1105) notes a double-meaning to Lot glancing to the east (Kedem) which can also mean "earlier." See what Rashi says: