I just came across the Tzror Hamor to Devarim 2:19 and it pointed me to a Gemara that elaborates upon the situation regarding Lot which clarifies everything! The Gemara is Nazir 23a. It says as follows:
- אלא משל ללוט ושתי בנותיו עמו הן שנתכוונו לשם מצוה וצדיקים ילכו בם הוא שנתכוין לשם עבירה ופושעים יכשלו בם ודלמא הוא נמי לשום מצוה איכווין אמר רבי יוחנן כל הפסוק הזה על שם עבירה נאמר (בראשית יג) וישא לוט (בראשית לט) ותשא אשת אדוניו את עיניה [את עיניו] (שופטים יד) כי היא ישרה בעיני וירא (בראשית לד) וירא אותה שכם בן חמור את כל ככר הירדן (משלי ו) כי בעד אשה זונה עד ככר לחם כי כלה משקה (הושע ב) אלכה אחרי מאהבי נותני לחמי ומימי צמרי ופשתי שמני ושיקויי והא מינס אניס תנא משום רבי יוסי בר רב חוני למה נקוד על וי"ו (בראשית יט) ובקומה של בכירה לומר שבשכבה לא ידע אבל בקומה ידע ומאי הוה ליה למיעבד מאי דהוה הוה נפקא מינה דלפניא אחרינא לא איבעי למישתי חמרא:
Rather is it illustrated by Lot when his two daughters were with him.21 To these [the daughters], whose intention it was to do right,22 [applies], 'the just do walk in them', whereas to him [Lot] whose intention it was to commit the transgression [applies], 'but transgressors do stumble therein'.
But perhaps it was his intention also to do right? — [Do not think this for a moment, for]23 R. Johanan has said: The whole of the following verse indicates [Lot's] lustful character. And Lot lifted up24 is paralleled by, And his master's wife lifted up her eyes upon;25 'his eyes' is paralleled by, for she hath found grace in my eyes26 'and beheld' is paralleled by, And Shechem the son of Hamor beheld her;27 'all the kikar ['plain'] of the Jordan' by For on account of a harlot, a man is brought to a kikar ['loaf'] of bread,'28 and 'fat' it was well watered everywhere' by, I will go after my lovers, that give me my bread and my water, my wool and my flax, mine oil and my drink.29
But [Lot] was the victim of compulsion?30 — It had been taught on behalf of R. Jose son of R. Honi that the dot31 over the letter waw [_ 'and'] in the word U-bekumah ['and when she arose']32 occurring in [the story of] the elder daughter, is to signify that it was her lying down that he did not notice, but he did notice when she arose. But what could he have done, since it was all over? — The difference is that he should not have drunk wine the next evening.
As Eliyahu Munk translated the Tzror Hamor:
- [...] The fact that the daughters of Lot had had noble intentions when making their father drunk before sleeping with him was appreciated by God, although their father's rescue from Sedom had been an act of pity, not a reward for merits Lot had accumulated. It is from here that the sages learned and taught us the principle of an illegal act performed for pure motives being superior to a meritorious act performed for a base motive. (Nazir 23)
Rabbi Chiya bar Abba uses this incident as the reason for stipulating that a person should use the earliest opportunity to perform a mitzvah, as the single night by which Lot's older daughter preceded her sister in sleeping with their father resulted in King David, and eventually the Messiah, a descendant of Ruth becoming part of her offspring. Not only that, but Ruth became a member of the Jewish people four generations sooner than her counterpart Naamah, the descendant of her younger sister.
To the question how we know that the daughters of Lot had such noble intent when sleeping with their father, we are told about this in Horiot 10 and Nazir 23 where the verse in Hoseah 14:10 כִּי-יְשָׁרִים דַּרְכֵי יְהוָה, וְצַדִּקִים יֵלְכוּ בָם, וּפֹשְׁעִים, יִכָּשְׁלוּ בָם 'for the paths of the Lord are smooth, the righteous can walk them whereas the sinners stumble on them' is interpreted as referring to Lot and his daughters. The daughters, who had noble intentions, were rewarded and could convert, whereas their father who had no such noble intentions was not rewarded. This enabled Boaz and the sages of his time (when the question of Ruth being able to convert arose) to interpret the prohibition by the Torah for members of the people of Ammon and Moav to ever join the Jewish people as applying only to the males of these nations, as the Torah wrote 'Amoni' and not 'Amonis' as well as 'Moavi' and not 'Moavis' (Deuteronomy 23:7).
~Tzror Hamor by Rabbi Avraham Saba, translated & annotated by Eliyahu Munk, pages 1792-1793
I've already lauded the Daughters of Lot once; hurrah x2 for this second proof of their virtue. It's amazing what far-reaching consequences the purity of one's thought or intention can have.