Following his circumcision, Abraham experiences the vision of the three angels.
"The Lord appeared to Abraham near the great trees of Mamre while he was sitting at the entrance to his tent in the heat of the day. Abraham looked up and behold! Three men standing nearby."
And behold three men: One to tell Sarah (about Isaac's birth) and one to overturn Sodom and one to heal Abraham, because one angel cannot accomplish two missions... Raphael, who healed Abraham went from there to rescue Lot.
(1) One angel cannot accomplish two missions? Why not? Says who? (besides Rashi, I mean.)
(2) One angel cannot accomplish two missions? Hello! Doesn't Rashi contradict himself when he says Rephael had two missions?
(3) If Rephael could be given a second mission after completing his first job, why are three angels needed, in the first place? Couldn't one single angel have given Sarah the good news, and then, having completed that mission, healed Avraham, and, with Avraham back in good health, gone on to destroy Sedom?
(4) So why not just send 4 angels, already? Is there a shortage, or something?
Metaphysics: We like to think that an angel is a baby-faced arrow-toting messanger from God, but perhaps we're wrong. Maybe an angel is the mission. The fact that Abraham was healed WAS itself the angel, by which I mean it was a manifestation of God's power. That's why an angel can't complete two tasks, because by definition the angel is the tast itself. This would explain why the angel that healed Abraham also saved Lot. In each case, it was the same power at work.
Purim Torah: Perhaps only three angels were sent because at first Lot wasn't going to be saved. Ok, so what changed?
In a utilitarian sense, Lot only matters because King David was his decendant, via Ruth. Ruth, you'll recall was from Moav, and according to the verse in Deuteronomy, Moabite men are banned from joining the Jewish people "because they didn't welcome you with bread and water on your journey from Egypt." Women, the Rabbis taught, have no obligation to welcome strangers; therefore, Moabite woman aren't included in the ban.
With me so far? Good.
Ok, how did the Rabbis know that woman aren't obligated to welcome strangers? The answer is in this week's sedra. When the angels appeared at Abraham's doorstep, only Abraham greeted them. Sarah stayed in the tent. Because Sarah stayed in the tent, a rule was established, going forward: Woman don't welcome guests. And with that rule established via Sarah's action, the way was paved for Ruth to enter the Jewish people. Suddenly, Lot was necessary and another angel was dispatched.