(Painting by Miriam Schulman)
Avrohom Avinu was the first to reveal the truth of Hashem's oneness in the world. Therefore, he merited everything included in Torah 9 of the second volume in Likutei Moharan (and Torah 7 in LM I). There, the Rebbe explains that through truth one is able to acquire Eretz Yisroel, prayer, faith in Hashem, and miracles. Avrohom merited these items through his sincerity and simplicity, for Avrohom always conducted himself with simplicity and with truth, as our sages say, "The one who walks with simplicity - this is Avrohom." (Makos 24b) Because of these traits that he possessed, Hashem commanded Avrohom to go to Eretz Yisroel. And, by going to Eretz Yisroel Avrohom then meritted perfected prayer and faith in Hashem to the point that he was worthy of being included in every Shmoneh Esrei, as in "Elokei Avrohom, etc." As such, anyone who desires to have perfect faith in Hashem and to pray to Him will say, "Elokei Avrohom."
The Torah relates that "Lot went with him [Avrohom]," (Bereishis 12:4) to explain that by definition darkness will always be bound to holiness, for Lot always followed after Avrohom to create darkness for him. Thus, we are taught that this is the main longing and service of the holy tzaddikim. The tzaddikim must work to reveal the truth hidden within the darkness of falsehood. This is the reason why Avrohom told Lot to separate from him - "If you go to the left I will go to the right." Avrohom was indicating to Lot that he did not want to walk in his path, for if Lot wanted to confuse Avrohom via the left side, which is related to evil desires and thoughts, then he would go to the right, which is the path of Torah and truth. However, if Lot preferred to go to the right, which in this case is the place of the evil inclination under the guise of mitzvos, then Avrohom conceded that he would go to the left, for nothing is worse then this falsehood of the "right".
This is why Hashem told Avrohom to "go for himself" (לך לך). Hashem implied that Avrohom should go to "himself" alone, to the essense of truth, which is Avrohom's essense and vitality.