Genesis 13:11

He went from being with Avraham and went to the west of Avraham. He traveled from east to west. The Madras says that he removed himself from the beginnings and said I don't want to have anything to do with Avraham or his G-d.

And Lot chose to him all the plain of Jardena; and Lot journeyed from the east, and they separated the one man from his brother.

ויבחר לו לוט, he selected as much area as he himself with his shepherds would manage to control as their grazing land. In this section of the earth Avram and his shepherds would not be allowed to graze.

ויסע לוט מקדם, he did not turn right or left which were north and south, but he moved from the east to the west to distance himself from Avram [the author translated מקדם as meaning “from the east,” though this is difficult to reconcile with the fact that the Jordan valley is east from the region of Bet El and Ai where Avram and Lot had been reported last in verse 3. The area of the Jordan valley was the area from which the Israelites under the leadership of Joshua would enter the land of Canaan (Joshua chapter 4)

ויבחר לו לוט את כל ככר הירדן, the reference is to one area within the Jordan valley, the use of the word כל here meaning that all the areas within that region were equally good as grazing land for his flocks.

ויסע לוט מקדם, in an easterly direction from the location where he had been with Avram. The river Jordan is east of the land of Canaan, being its eastern boundary. We already explained the letter מ in the word מנגב in 13,3 as meaning “in a southerly direction,” here too the letter מ in the word מקדם means “in an easterly direction.” [the author does not want us to think that the letter מ in either word means “away from,” as if it did the verse would not make sense. Ed.]

ויפרדו איש מעל אחיו, Lot’s traveling towards the Jordan valley resulted in these two brothers separating from one another. Seeing that it was Lot who severed the relationship, it seems strange that the Torah describes it as איש מעל אחיו, “one from another,” as if they were both separating from one another. The Torah describes not the parting, but the result of the parting; after Lot had moved they were in effect apart from one another. Now Avram was a resident of the land of Canaan, whereas Lot had become a resident of the cities in that valley, i.e. he no longer shared Avram’s destiny in the land of Canaan. Even though both were essentially nomads, moving with their herds and flocks, their home bases were different from one another. Lot, although aware of the evil reputation of the people in the cities of that valley, had decided to ignore this, preferring to concentrate on the advantages offered by the land itself.