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.
Now, we have not just one very rich man, but we have two. Lot is not called very rich, but he was also quite well off.
