I don't know the exact sources but I remembered some commentaries from the Malbim and Vilna Gaon which point out a difference between 'את'-based words and 'עם'-based words (both translated to mean 'with') in the stories of Lot and Avram and the story of Bilaam.
Could someone explain me the motives for using the et or im version of 'with' in these specific verses according to these or other commentaries?
According to HaKtav v'HaKabala (Genesis 13:14) when Lot was good (as in 12:4), and in that sense similar to Avraham, the term אתו 'ito' is used, indicating that the two things are similar. When Lot was not righteous (as in 13:1), and went with Avraham, עמו 'imo' is used, to indicate that he was with him, but not similar to him, but rather secondary to him. See also HaKtav v'HaKabala to Genesis (24:32).
He uses the same approach to explain the episode of Balak, but seems to reverse himself on the definitions of 'ito' and 'imo' respectively. First God tells Bil'am not to go with Balak's men (Numbers 22:12). However, later God tells him the opposite; to join Balak's men (22:20). HaKtav V'HaKabbalah (22:12) explains this based on the aforementioned distinction between עמו (imo) and אתו (ito). 'Imo' is used when two things together are similar; not merely juxtaposed. 'Ito' is used for things that find themselves together but are not themselves similar. When God told Bil'am not to go with them he said לֹ֥א תֵלֵ֖ךְ עִמָּהֶ֑ם, using the root עמו. This meant that he shouldn't go together with them, united in purpose to curse the Jews. However, when God told him to go he said ק֖וּם לֵ֣ךְ אִתָּ֑ם using the root אתו. This meant that he should merely go with them; but not join them in going for the purpose of cursing the Jews.
In several places, however, Malbim writes the exact opposite (e.g. Genesis 24:54, Exod. 21:3): that עמו indicates that the two things are similar, while אתו indicates something secondary to something else.
Malbim explains (commentary to 12:4) that (12:4) uses אתו since Lot was not similar to Avraham. Avraham was purposefully traveling away from his homeland as commanded by God. Lot was just tagging along. He explains that (13:1) uses עמו since in that case he and Avraham were equals; they were going with each other, as opposed to one tagging along. This was because Lot was also rich and was therefore independent.
This might help to answer your question
In addressing this question, the Netziv shares his own observations about the differences between going “et” versus going “im.” Following on his coattails, perhaps in the specific context of people traveling together, this distinction applies. Those who go “et” others, are walking on the same path, but their minds are in different places. Those who walk “im” others, not only share a physical space but also share a mental and perhaps spiritual state of being.
People who go “et” others (different mindsets) in the Torah include: Terach with his family on the way to Haran; Lot going with Avram on his continued journey to Canaan; Lot immediately before the fight that caused him to separate from Avraham; Avraham with his lads to sacrifice his son. Avimelekh and company, as they depart from Yitzchak after making a treaty; Yaakov and his sons when they went to Egypt, all with different hopes for the future; the Egyptians who came with Yosef to bury Yaakov.
People who go “im” others (same mindset) in the Torah include: Lot going with Avram after the events in Egypt (after seeing G-d help Avram in a tight situation) [soon after, Lot separates “me’imo” to move to S’dom]; Avraham accompanying the angels on their way to destroy S’dom; Lot and his daughters escaping from S’dom; Eliezer and the servants looking to find a wife for Yitzchak; Rivka’s choice to go with Eliezer to be Yitzchak’s wife; Yaakov with Lavan (until he is no longer “imo” (Bereishit 31:2); 400 men with Eisav; the brothers of Yosef when they go to bury their father.
It is interesting to note that like Bilaam, Lot is the main figure who jumps back and forth. Perhaps this is because, like Bilaam, he was an opportunist who came close when it was good for him, but distanced himself when things did not work out.
P.s. The difference was once described to me as 'beside him' and 'with him' for 'with him' indicates equality, while 'beside him' will tell us that one is the principal.
In Hebrew, 'ito’ has its word root as 'et’. 'The word 'et’ is used to precede a subject in order to give emphasis to the subject. In its very essence, then, 'et’is subordinate. When Lot was originally with Abram he knew his role. Abram was the wise, talented, teacher and leader. Lot was the faithful, trusted, and able student. In order to succeed in virtually anything, one has to know his talents and limitations. Imagine an offensive lineman in football who thinks he is the quarterback. Or imagine a gifted auto technician who thinks he is the CEO. Such people will not only fail in their dream positions, they will also fail in the jobs in which they are truly talented. Lot went from a proper perspective of 'Ito’ –first Abram which means subordination – to a disastrous one of 'Imo’. 'Imo’ means I am with you as an equal. When Lot returned from Egypt laden with wealth and resources, he became ’Imo’-in this verse Lot is written before the word ’Imo’. He no longer viewed himself as subordinate to Abram.
