The separation between Abram and Lot comes after the events recorded in Genesis 12:1–20. Abram had gone to stay for a while in Egypt to escape the hunger in Canaan. There Abram lied that Sarai was his sister, to avoid being killed for the sake of his wife. When Pharaoh discovered this, he sent Abram away. All this time, Lot was with Abram. Immediately after the separation between Abram and Lot in Genesis 13:1–18, we see Abram in Genesis 14:1–24 going on a rescue mission to rescue Lot after the cities Lot had been living among were attacked and raided.
1 So Abram went up from Egypt, he and his wife and all that he had, and Lot with him, into the Negeb.