Rabbi Yudan in the name of Rabbi Eivo: the firstborn, because she disgraced her father's honor by saying "Moab" ["from father"], Scripture said, "Do not provoke them to war" (Deuteronomy 2:9) - but you may divert their rivers and set their grain-stacks on fire. But the younger, because she spared her father's honor and said "Ben-Ammi" ["son of him who was with me"], "do not provoke them to war" at all. Rabbi Yehuda bar Simon and Rabbi Chanin said in the name of Rabbi Yochanan: the daughters of Lot were going to commit a transgression, and yet they were granted children. By whose merit? By the merit of Abraham. "Moab" - from "father" (av); "for a father of a multitude of nations I have made you" (Genesis 17:5).
The Daughter Who Guarded Her Father's Honor Was Spared
Yalkut Shimoni on Torah 87:2
רַבִּי יוּדָן בְּשֵׁם רַבִּי אֵיבוֹ הַבְּכִירָה עַל יְדֵי שֶׁבִּזְּתָה כְּבוֹד אָבִיה אָמְרָה מוֹאָב אָמַר הַכָּתוּב, "אַל תִּתְגָּר בָּם מִלְחָמָה", אֲבָל אַתָּה מְפַתֵּק נְהָרוֹת שֶׁלָּהֶן וּמֵצִית גְּדִישִׁין שֶׁלָּהֶן בָּאֵשׁ, אֲבָל הַצְּעִירָה עַל יְדֵי שֶׁחָסְתָה עַל כְּבוֹד אָבִיהָ וְאָמְרָה בֶּן עַמִּי בֶּן מִי שֶׁהָיָה עִמִּי (שם יט) ("וְ)אַל תִּתְגָּר בָּם" (מִלְחָמָה) כָּל עִיקָר. אָמַר רַבִּי יְהוּדָה בַּר סִימוֹן וְרַבִּי חַנִין בְּשֵׁם רַבִּי יוֹחָנָן, בְּנוֹתָיו שֶׁל לוֹט הוֹלְכוֹת לַעֲבֹר עֲבֵירָה וְנִתְפַּקְּדוּ, בִּזְכוּת מִי, בִּזְכוּת אַבְרָהָם, מוֹאָב מֵאָב (בראשית יז, ה) "כִּי אַב הֲמוֹן גּוֹיִם נְתַתִּיךָ".