We see that Avraham cares for Lot, as is shown in bereishis perek 14, where Avraham goes after 4 kings in order to save Lot. Why then, when Hashem tells Avraham that He's going to destroy Sodom, doesn't He say that He'll save Lot? Also, why doesn't Avraham ask Hashem what Lot's fate will be?

(Inspired by this comment by @Ari) In [Shabbat 12a], a difference in opinions is brought regarding whether one may kill a louse on Shabbat. The discussion culminates in a debate between בית שמאי and בית הלל, the latter of which, as usual, rules leniently. Since we generally follow the ruling of ב...