The Gemara discusses the place and function of 'Hashem sefatai tiftach' as a verse attached to the Amidah, supplying the core Talmudic basis for the question.
אָמְרִי: כֵּיוָן דְּתַקִּינוּ רַבָּנַן ״הַשְׁכִּיבֵנוּ״ — כִּגְאוּלָּה אֲרִיכְתָּא דָּמְיָא. דְּאִי לָא תֵּימָא הָכִי, שַׁחֲרִית הֵיכִי מָצֵי סָמֵיךְ? וְהָא אָמַר רַבִּי יוֹחָנָן: בַּתְּחִלָּה אוֹמֵר: ״ה׳ שְׂפָתַי תִּפְתָּח״, וּלְבַסּוֹף הוּא אוֹמֵר: ״יִהְיוּ לְרָצוֹן אִמְרֵי פִי״. אֶלָּא הָתָם כֵּיוָן דְּתַקִּינוּ רַבָּנַן לְמֵימַר ״ה׳ שְׂפָתַי תִּפְתָּח״ — כִּתְפִלָּה אֲרִיכְתָּא דָּמְיָא. הָכָא נָמֵי, כֵּיוָן דְּתַקִּינוּ רַבָּנַן לְמֵימַר ״הַשְׁכִּיבֵנוּ״ — כִּגְאוּלָּה אֲרִיכְתָּא דָּמְיָא.
They say in response: Since the Sages instituted the practice of reciting: Help us lie down, it is considered one extended blessing of redemption, and therefore does not constitute an interruption. As if you fail to say that the sections added by the Sages are considered no less significant than the original prayers, then can one juxtapose redemption to prayer even in the morning? Didn’t Rabbi Yoḥanan say: Before every prayer one recites the verse: “Lord, open my lips, that my mouth may declare Your glory” (Psalms 51:17) as a prelude to prayer? Afterward, one recites the verse: “May the words of my mouth and the meditations of my heart be acceptable before You” (Psalms 19:15). Doesn’t the verse: Lord, open my lips, constitute an interruption between redemption and prayer? Rather, there, since the Sages instituted that one must recite: Lord, open my lips, it is considered as an extended prayer and not as an interruption. Here, too, with regard to the evening prayer, since the Sages instituted to recite the blessing Help us lie down, it is considered as one extended blessing of redemption.
