Did Lot have sons?

Question

When the angels ask Lot to warn his relatives about the catastrophe Bereshis 19:12:

Then the agents said to Lot, “Whom else have you here? Sons-in-law, your sons and daughters, or anyone else that you have in the city—bring them out of the place.

Rashi comments the word sons as

ובניך THY SONS means the sons of your married daughters. The Midrashic explanation of עוד YET is: since they have perpetrated so disgraceful an act, can you yet be so bold (more literally, “can you yet open your mouth”) to speak in defence of them? — for the whole night through he had been talking in favor of them. To obtain this explanation you must read: עוד מי לך פֶּה Have you yet a mouth! (instead of פֹּה here) (Genesis Rabbah 50:5).

From Rashi on Bereshis 19:14 we learn that Lot had 2 married daughters who lived with their husbands and two daughters at home who were betrothed at the time that the angels came to visit Lot. Furthermore, from Pirkei d'Rabbi Eliezer 25:8 and Sefer haYashar Veyera 5-6 we learn a tragic story about Lot's daughter Paltith, who was brutally murdered for trying to help a destitute man. Thus, Lot was a father of 5 daughters, but seemingly no sons.

How could the meforshim be sure that Lot did not have any sons?

Answer 1

Thanks to the comment of @Fred we have two comments on the quoted Rashi, which answer the question:

Sifsei Chakhamim by R' Shabbethai ben Yosef Bass (Strom) also known as Mishorer (poet) quoting R' Eliyahu Mizrachi:

בני בנותיך הנשואות. ואם תאמר מנא ליה לרש"י דילמא בניו היו ולא בני בניו ויש לומר מדכתיב חתן תחילה ואח"כ בניך ובנותיך משמע דקאי בניך ובנותיך על חתן דהיינו בנות הנשואות:

Your married daughter’s sons. You might ask: How does Rashi know this? Perhaps they were his sons and not his grandsons! The answer is: Since it is written “son-in-law” first, followed by “your sons, your daughters,” it implies that “your sons, your daughters” refers back to “son-inlaw,” i.e., the married daughter’s sons.

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Alternatively, Gur Aryeh by R' Yehuda Loew ben Betzalel (Maharal):

דהא בודאי מלאכים היו, ויודעים היו שאין לו בנים, כדמוכח קרא (פסוק יד) שלא רצה לוט להציל רק חתניו, ואם כן למה אמר "ובניך".

The visitors for sure were angels and they knew that Lot did not have sons, as the verse Bereshis 19:14 states that Lot ran to save only his sons-in-law, that is why the verse says "and your sons".

In both of these cases we have to also mention the midrash Bereshis Rabbasi Vayishlach 12 (see translation here) about father's feeling towards his children. I.e. if Lot had sons he would not avoid saving them.

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There is also midrash Pirkei D'Rabbi Eliezer 25:11:

עירית אשתו של לוט נכמרו רחמה על בנותיה הנשואות והביטה לאחריה לראות אם הולכות אחריה אם לא (וראת אחרי) [וראתה אחריה] השכינה ונעשית נציב מלח, שנאמר ותבט אשתו מאחריו ותהי נציב מלח:

The pity of 'Edith (Irith) the wife of Lot was stirred for her daughters, who were married in Sodom, and she looked back behind her to see if they were coming after her or not. And she saw behind the Shekhinah, and she became a pillar of salt, as it is said, "And his wife looked back from behind him, and she became a pillar of salt" (Gen. 19:26)

We could accept it as a proof that the midrash does not mention her sons. But is it possible that she did not like her sons and did not want to have mercy on them? In view of the gemara Nidda 31a we can reject this point as well:

וא"ר יצחק אשה מזרעת תחל' יולדת זכר איש מזריע תחלה יולדת נקבה

Rabbi Yitzḥak says that Rabbi Ami says: (The sex of a fetus is determined at the moment of conception). If the woman emits seed first, she gives birth to a male, and if the man emits seed first, she gives birth to a female, as it is stated: “If a woman bears seed and gives birth to a male” (Leviticus 12:2).

I.e. naturally a woman has a stronger connection to her son, while a man to his daughter. Because in the midrash the Lot's wife got stirred for her daughters and not sons, she did not have any sons.