given the situation when "all the men of the city, both young and old" assemble in a mob to threaten Lot's household in an attempt to gain the bodies of the angles for their own nefarious means, i am going to make the educated guess that Lot's sons were not particularly righteous dudes.
i'm going to guess that Lot is not an idiot
therefore i guess he knew more or less what kind of people his sons were
therefore i am going to guess that, based on his worldly wisdom, of which i presume he had much, that he didn't bother even approaching them seriously; that he figured it was a wasted effort i he would have.