After all of Abraham's wondorous prayers to Hashem to save Sodom the posuk says (י״ח:לג):
וַיֵּ֣לֶךְ יְהוָ֔ה כַּאֲשֶׁ֣ר כִּלָּ֔ה לְדַבֵּ֖ר אֶל־אַבְרָהָ֑ם וְאַבְרָהָ֖ם שָׁ֥ב לִמְקֹמֽוֹ
God 'went' when he had finished speaking to Avrohom and Avrohom returned to his place.
Rashi says:
ואברהם שב למקומו. נִסְתַּלֵּק הַדַּיָּן נִסְתַּלֵּק הַסָּנֵגוֹר, וְהַקָּטֵיגוֹר מְקַטְרֵג וּלְפִיכָךְ וַיָּבֹאוּ שְׁנֵי הַמַּלְאָכִים סְדֹמָה, לְהַשְׁחִית
Avrohom returned to his place - The Judge departed, the defender departed so the accuser accused. Therefore "The two angels came to Sodom" - to destroy.
In short, Avrohom's prayers did not save Sodom.
Yet a bit later the posuk says (י״ט:כ & י״ט:כא):
וַיֹּ֥אמֶר ל֖וֹט אֲלֵהֶ֑ם אַל־נָ֖א אֲדֹנָֽי...הִנֵּה־נָ֠א הָעִ֨יר הַזֹּ֧את קְרֹבָ֛ה לָנ֥וּס שָׁ֖מָּה וְהִ֣יא מִצְעָ֑ר אִמָּלְטָ֨ה נָּ֜א שָׁ֗מָּה הֲלֹ֥א מִצְעָ֛ר הִ֖וא וּתְחִ֥י נַפְשִֽׁי
And Lot said: "Please no! My Master behold this city is near to flee there and it is small. Let me flee there. Is it not small! and my soul shall live."
Hashem replied:
וַיֹּ֣אמֶר אֵלָ֔יו הִנֵּה֙ נָשָׂ֣אתִי פָנֶ֔יךָ גַּ֖ם לַדָּבָ֣ר הַזֶּ֑ה לְבִלְתִּ֛י הָפְכִּ֥י אֶת־הָעִ֖יר אֲשֶׁ֥ר דִּבַּֽרְתָּ׃
And He said to him:"Behold I have accepted thee concerning this thing also, not to destroy the city, as you have spoken"
Is this not a wonder!? Lot the רשע who was ready to live in the immoral city of Sodom, ready to give up his own daughters to strangers to abuse them, his תפילות were answered, yet the holy אברהם אבינו -צדיק's תפילות did not cause Hashem to save Sodom?!