They were actually traveling northeast here, and the reference of going to the south was going south of the Promised Land to the Negev, probably in the area of Beersheba, if your familiar with a map of Israel.
Abraham separated from Ur, was separated from his father’s house, from Terah, he was separated from Egypt now, and now he is going to be further separated from his kindred, from Lot his nephew. It is interesting to note, as we look at this in passing (we will get to it a little bit later here), but it was not until after Abraham was separated from Lot, that God told Abram to “lift up your eyes and see the land which I am going to give you.” It is entirely possible, since the promised seed had not been given yet, that Abraham might have had Lot in the back of his mind as a possible heir. God is going to show Abraham that Lot is not the heir and they are going to separate.
Now he was tagging along, Lot walked with Abraham. But spiritually, Lot just did not have it. But for a while, as long as he was walking with Abraham, it appears as though he might have had it. He was at one, but it could not last.
When it says he went to the south, you know if you went south from Egypt you would go to Ethiopia. But it means he went to the south of the land of Canaan, to the Negev, into the area of Beersheba. But he did not stop in Beersheba.