Dear Rabbi, I found out that the Vilna Gaon traces the meaning of the word ’et’ - to join a person - more physically than philosophically. The word ’im’ denotes a closer relationship; i.e. one with kindred spirit. So one would assume Lot went the fitst time just physically with Avram, while the second time they had a stronger connection. If one would look at it this way it seems logical that the Torah writes after the strife (verse 8) the offered separation (verse 9) and Lot Chosing to move to the area of Sodom and a piece of Land which reminded him of Egypt that verse 13:14 reads that Lot went m’imo from being with Avram; in other words; he no longer was one-minded, no longer sharing the same aspects, the same way of live. So is imo a negative or positive description? Or does this depends on the context? For in the case of Bilaam it seems obvious that it’s negative.
That explanation is especially fitting in the case of Lot and Bil’am. To be im (ideologically with) is positive when the context is positive, but it’s negative to be “ideologically with” one who is negative. Accordingly, God begrudgingly allows Bila’m (Bamidbar 22, 20) to go “et” (physically with, but not ideologically with) the evil Moabites who tried to get him to curse Israel, but Bil’am showed his evil side when he went “im” them (with them ideologically), wanting to curse Israel (ibid, 21).