Why did Lot's separation from Avraham warrant a repetition of God's promise to Avraham? 

Whereas Avraham may have thought that he would ccomplish his mission together with the assistance of Lot, he is now informed that he must go about this struggle on his own.

Parashat Lekh-Lekha tells of the separation between Avraham and his nephew, Lot. Unable to manage together given the vast wealth they accumulated, they decide to part ways, with Lot choosing to relocate in the corrupt city of Sedom, while Avraham remains in the region west of Sedom, in the Judean Hills. (See 13:5-13.)

After Lot's departure, God appears to Avraham and reiterates His promise to give the Land of Canaan to Avraham's offspring: "The Lord said to Avraham after Lot had parted from him: Raise your eyes and look out from the place where you are… for I give all the land that you see to you and your offspring forever… " (13:14-15). The Torah's introduction to this promise, "The Lord said to Avraham after Lot had parted from him," suggests a connection between this promise and Lot's recent departure. Wherein lies this connection? Why did Lot's separation from Avraham warrant a repetition of God's promise to Avraham?

Rashi, based on the Midrash Tanchuma, explains that in truth, Lot's separation did not necessitate God's reiteration of His promise, but rather allowed it, it made it possible. Meaning, God wanted to remind Avraham of His promise, but the presence of Lot, whom Rashi describes here as a "rasha" (wicked person), precluded the possibility of a divine revelation to Avraham. Only once Lot left Avraham's side could God once again reveal Himself to Avraham and repeat His promise.

Radak suggests a different explanation, claiming that God here informs Avraham that he alone will inherit the land. Lot himself no longer enjoys any rights to Eretz Canaan, and no one else will take Lot's place alongside Avraham. Rather, Avraham alone with receive rights to the land and bequeath it to his offspring.

An interesting variation of this approach appears in the work "Tishbi," by Rav Shraga Pollak. He suggests that after Lot's departure, Avraham felt uneasy about his sudden solitude, he was intimidated by the prospect of having to embark on his mission alone, without anyone at his side. How can he hope to spread the teachings of ethical monotheism in a pagan world without any assistance?

God therefore reassures him, "Look out from the place where you are… " From this very situation, from the solitude and isolation Avraham currently experiences, he will inherit Canaan and build a nation that will represent his values. God here informs Avraham that throughout his descendants' history, they will be subjected to loneliness and seclusion, they must engage in a bitter struggle against the entire world, with little if any support or assistance from without. Many years later, the sorcerer Bilam describes Am Yisrael as, "a people that dwells apart, not reckoned among the nations" (Bamidbar 23:9). This is the destiny of the Jewish people – a destiny of distinction and aloneness. Lekh-Lekha describes Avraham as "Avram ha-ivri" – "Avram the Hebrew" (14:13). Chazal explain this expression to mean, "He stands on one side ['ever echad'], and the entire world stands on the other." Whereas Avraham may have thought that he will accomplish his mission together with the assistance of Lot, he is now informed that he must go about this struggle on his own – a symbol of the isolation with which his progeny will have to contend for millennia to come.