When Abraham and Lot separate in Genesis 13, Abraham tells Lot:
הֲלֹא כָל-הָאָרֶץ לְפָנֶיךָ, הִפָּרֶד נָא מֵעָלָי: אִם-הַשְּׂמֹאל וְאֵימִנָה, וְאִם-הַיָּמִין וְאַשְׂמְאִילָה.
"Is the whole land not before you? Now separate from me. If to the left, I will go right; if to the right, I will go left."
Targum Unkelos, the Authorized Translation of Chumash according to the Talmud renders 13:9 as
הֲלָא כָּל אַרְעָא קֳדָמָךְ, אִתְפָּרַשׁ כְּעַן מִלְּוָתִי: אִם אַתְּ לְצִפּוּנָא אֲנָא לְדָרוֹמָא, וְאִם אַתְּ לְדָרוֹמָא וְאַצְפְּנָךְ.
Is the whole land not before you? Now separate from me. If to the north, I will go south; if to the right, I will go north.
If north is on their left, and south is on their right, that means that Abraham and Lot were heading east, or towards the Mediterranean coast from (what was later to be) Ammon and Moab, and not north from Egypt as is implied.
With that introduction, my question is: do we have any sources for why they took the long way up from Egypt, and what happened between them leaving Egypt and separating somewhere near Sodom (somewhere near the present day dead sea according to Medrash)?