Genesis 12:4 reads: Vayelech Avram... Avram went according as HaShem had sproken to him, vayelech Lot oto אתו, and Lot went with him. But the next verse reads: Vayikach Avram.. et Lot, and Avram took Lot, vayetzu lalechet, and they went out on their way to... Genesis 13:1 again describes both men going on their way, but this time it says Vaya’al Avram... v’Lot imo עמו, and Avram went up, and Lot with him. So what’s the difference, when does one use אתו and when עמו, because both are translated as ’with him’.
The Malbim (Sefer HaCarmel, p. 50) explains the slight difference as follows: Imo means that the two are totally equal on the issue, as opposed to Ito, which means that one of the two is the more active on the topic, and the second is more passive and secondary. In this case, Avraham is generally the major figure, and Lot went with him: Ito. On the other hand, on their way up from Egypt, both of them equally wanted to leave Egypt, and Lot had his own wealth, property, and importance as well, so it says: Imo.