In the plain reading of Genesis 19 and 20, it's unclear if Abraham knows Lot survived.
Given that, consider Abraham's view: He pleads with God for mercy, to which God said "ok, for the sake of so few, I'll spare the cities," but then the cities are destroyed. Abraham got up in the morning to see smoke billowing up.
What must Abraham think?
Perhaps this goes unresolved for Abraham. And perhaps life is like that sometimes.