The Steipler writes in the introduction to Chayei Olam that discussions about theology with those who do not share our beliefs usually fails. He illustrates this by pointing to the story of the angels who came to destroy Sdom. When the people of Sdom approached Lot's door to demand that he turn over their guests, the angels smote the population with blindness and they could no longer even find the entrance to Lot's home. Yet, shortly thereafter, when Lot tells his sons-in-law that these same angels have come to destroy the city, "veye'hi k'metzachek...", they thought Lot foolish. They did not have even a shred of doubt that Lot was wrong and misguided even though they had earlier witnessed these same angels exerting supernatural power. If they ignored the evidence of their own eyes, what could he possibly have said to convince them?
The Steipler does not stress this point, but it seems that the reason why Lot's sons-in-law went astray was the midah of "tzechok" - frivolity, lightheartedness, taking everything as a joke. It's not that they were philosophically disenchanted with Lot's religious beliefs (whatever they were), but rather they simply did not take things seriously enough to give religion and philosophy much thought. Had Lot spent more time trying to convince them of the seriousness of what was at stake it would have probably just given them more to mock at. The Mesilas Yesharim writes (ch 5.) that leitzanus is like a shield greased with oil that causes the arrows of hisorerus to simply fall away (see also Sichos Mussar of R' Chaim Shmuelivitz, 5731 #21).
Contrast the reaction of Lot's sons-in-law with a different tzechok later in Braishis: when Sarah finally gives birth to Yitzchak she declares, "tzechok asah li Elokim, kol ha'shomea yitzachak li." Lot's sons-in-law turned G-d's word into something to be mocked; G-d mocks the naysayers and doubters who said Sarah could not have children.
Elul is the antithesis of tzechok. The ba'alei mussar would examine every detail of life with seriousness and great introspection as the days of Rosh haShana approached. Having not had the privilege of learning in a yeshiva with an intensive mussar program, I find this a hard mindset to absorb or imagine; I cannot imagine the thoughts of a R' Yisrael Salanter or a R' Simcha Zissel as they prepared for the Yamim Noraim.