Another interpretation: "these are divine beings" [Lot recognized them as angels]. "For this reason they have come under the shadow of my roof" (Genesis 19:8): not by my own merit, but by the merit of Abraham.
They Came Under My Roof by Abraham's Merit
Yalkut Shimoni on Torah 84:4
דָּבָר אַחֵר אֱלֹהוּת הֵן אֵלוּ כִּי עַל כֵּן בָּאוּ בְּצֵל קֹרָתִי, לֹא בִּזְכוּתִי אֶלָּא בִּזְכוּת אַבְרָהָם.