Does לא בשמים היא mean that anything goes and we can do whatever we want?
1א

Note that the underlines are mine and are not in the original sources.

2ב
(יא) כִּ֚י הַמִּצְוָ֣ה הַזֹּ֔את אֲשֶׁ֛ר אָנֹכִ֥י מְצַוְּךָ֖ הַיּ֑וֹם לֹֽא־נִפְלֵ֥את הִוא֙ מִמְּךָ֔ וְלֹ֥א רְחֹקָ֖ה הִֽוא׃ (יב) לֹ֥א בַשָּׁמַ֖יִם הִ֑וא לֵאמֹ֗ר מִ֣י יַעֲלֶה־לָּ֤נוּ הַשָּׁמַ֙יְמָה֙ וְיִקָּחֶ֣הָ לָּ֔נוּ וְיַשְׁמִעֵ֥נוּ אֹתָ֖הּ וְנַעֲשֶֽׂנָּה׃ (יג) וְלֹֽא־מֵעֵ֥בֶר לַיָּ֖ם הִ֑וא לֵאמֹ֗ר מִ֣י יַעֲבָר־לָ֜נוּ אֶל־עֵ֤בֶר הַיָּם֙ וְיִקָּחֶ֣הָ לָּ֔נוּ וְיַשְׁמִעֵ֥נוּ אֹתָ֖הּ וְנַעֲשֶֽׂנָּה׃ (יד) כִּֽי־קָר֥וֹב אֵלֶ֛יךָ הַדָּבָ֖ר מְאֹ֑ד בְּפִ֥יךָ וּבִֽלְבָבְךָ֖ לַעֲשֹׂתֽוֹ׃ (ס)

(11) Surely, this Instruction which I enjoin upon you this day is not too baffling for you, nor is it beyond reach. (12) It is not in the heavens, that you should say, “Who among us can go up to the heavens and get it for us and impart it to us, that we may observe it?” (13) Neither is it beyond the sea, that you should say, “Who among us can cross to the other side of the sea and get it for us and impart it to us, that we may observe it?” (14) No, the thing is very close to you, in your mouth and in your heart, to observe it.

3ג

ר' יצחק אמר מהכא (דברים ל, יד) כי קרוב אליך הדבר מאד בפיך ובלבבך לעשותו אימתי קרוב אליך בזמן שבפיך ובלבבך לעשותו

Rabbi Yitzḥak said that this idea is derived from here: “But the matter is very near to you, in your mouth and in your heart, that you may do it” (Deuteronomy 30:14). When is it very near to you? When it is in your mouth and in your heart, that you may do it, i.e., when you articulate your Torah study.
4ד
5ה

והיינו דאמר אבדימי בר חמא בר דוסא מאי דכתיב (דברים ל, יב) לא בשמים היא ולא מעבר לים היא לא בשמים היא שאם בשמים היא אתה צריך לעלות אחריה ואם מעבר לים היא אתה צריך לעבור אחריה

And this idea, that one must exert great effort to retain one’s Torah knowledge, is in accordance with what Avdimi bar Ḥama bar Dosa said: What is the meaning of that which is written: “It is not in heaven…nor is it beyond the sea” (Deuteronomy 30:12–13)? “It is not in heaven” indicates that if it were in heaven, you would have to ascend after it, and if it were beyond the sea, you would have to cross after it, as one must expend whatever effort is necessary in order to study Torah.

6ו

Ibn Ezra - Spain, 1089-1164

7ז
(א) בפיך ובלבבך. שכל המצות עיקרם הלב ויש מהם זכר בפה לחזוק הלב ויש מעשה כדי שיזכור בפה:

(1) in your mouth, and in your heart The essence of all the commandments is in one’s heart; but they also entail deeds, so that one may recall them with the words of one’s mouth.

8ח

Rambam / Maimonides - Spain, Morocco, Egypt, 1137-1204

9ט
רְשׁוּת לְכָל אָדָם נְתוּנָה. אִם רָצָה לְהַטּוֹת עַצְמוֹ לְדֶרֶךְ טוֹבָה וְלִהְיוֹת צַדִּיק הָרְשׁוּת בְּיָדוֹ. וְאִם רָצָה לְהַטּוֹת עַצְמוֹ לְדֶרֶךְ רָעָה וְלִהְיוֹת רָשָׁע הָרְשׁוּת בְּיָדוֹ. הוּא שֶׁכָּתוּב בַּתּוֹרָה (בראשית ג כב) "הֵן הָאָדָם הָיָה כְּאַחַד מִמֶּנּוּ לָדַעַת טוֹב וָרָע". כְּלוֹמַר הֵן מִין זֶה שֶׁל אָדָם הָיָה יָחִיד בָּעוֹלָם וְאֵין מִין שֵׁנִי דּוֹמֶה לוֹ בְּזֶה הָעִנְיָן שֶׁיְּהֵא הוּא מֵעַצְמוֹ בְּדַעְתּוֹ וּבְמַחֲשַׁבְתּוֹ יוֹדֵעַ הַטּוֹב וְהָרַע וְעוֹשֶׂה כָּל מַה שֶּׁהוּא חָפֵץ וְאֵין מִי שֶׁיְּעַכֵּב בְּיָדוֹ מִלַּעֲשׂוֹת הַטּוֹב אוֹ הָרַע. וְכֵיוָן שֶׁכֵּן הוּא פֶּן יִשְׁלַח יָדוֹ:

Every person was endowed with a free will; if he desires to bend himself toward the good path and to be just it is within the power of his hand to reach out for it, and if he desires to bend himself to a bad path and to be wicked it is within the power of his hand to reach out for it. This is known from what it is written in the Torah, saying: "Behold, the man is become as one of us, to know good and evil" (Gen. 3.22), that is as if saying: "Behold, this species, man, stands alone in the world, and there is no other kind like him, as regards this subject of being able of his own accord, by his reason and thought, to know the good and the evil, and to do whatever his inclination dictates him with none to stay his hand from either doing good or evil; and, being that he is so, 'Lest he put forth his hand, and take also from the tree of life, and eat, and live forever'" (Ibid.)1Abodah Zarah, 16b; Megillah, 25a. G.

10י

Sforno - Italy, 1470-1550

11יא
(ב) לא נפלאת היא ממך. שתצטרך לנביאים.

(2) לא נפלאת היא ממך, so that you would need to ask the prophets in order to understand it correctly.

12יב

Contemporary Halakhic Problems, Vol. I, Introduction, The Methodology of Halakhah 4.

Rabbi David Bleich, 1977

Although the Torah itself is immutable, the Sages teach that the interpretation of its many laws and regulations is entirely within the province of human intellect. Torah is divine but "lo ba-shamayim hi—it is not in the heavens" (Deut. 30:12); it is to be interpreted and applied by man. A remarkable corollary to the principle of the immutability of the Torah is the principle that, following the revelation at Sinai, no further heavenly clarification of doubt or resolution of ambiguity is possible. Clarification and elucidation are themselves forms of change. Since there can be no new revelation, a prophet who claims the ability to resolve disputed legal points by virtue of his prophetic power stands convicted by his own mouth of being a false prophet.

13יג

Rav Moshe Feinstein, 1895-1986. Responsa from 1959

14יד
אבל הוא מטעם שהנכון לע״ד בזה שהיו רשאין ומחוייבין חכמי דורות האחרונים להורות אף שלא היו נחשבין הגיע להוראה בדורות חכמי הגמ׳ שיש ודאי לחוש אולי לא כיוונו אמיתות הדין כפי שהוא האמת כלפי שמיא אבל האמת להוראה כבר נאמר לא בשמים היא אלא כפי שנראה להחכם אחרי שעיין כראוי לברר ההלכה בש״ס ובפוסקים כפי כחו בכובד ראש וביראה מהשי״ת ונראה לו שכן הוא פסק הדין הוא האמת להוראה ומחוייב להורות כן אף אם בעצם גליא כלפי שמיא שאינו כן הפירוש, ועל כזה נאמר שגם דבריו דברי אלקים חיים מאחר שלו נראה הפירוש כמו שפסק ולא היה סתירה לדבריו. ויקבל שכר על הוראתו אף שהאמת אינו כפירושו.

However, in my humble opinion, [the scholars of earlier generations,] despite their inferiority when compared to the Torah scholars of [still] earlier generations, and, therefore, their concern lest they rule in error—an error known to Hashem—did not refrain from assuming the obligation to do so. The Torah instructs us, "It is not in heaven" [Deuteronomy 30:12]. Each posek must rule as he sees fit, after meticulous study and analysis of all the relevant texts and prior rulings, to the best of his ability, fully cognizant of the heavy responsibility he has assumed in applying Hashem's Torah to the life of the Jew. If, after all his efforts, his ruling does not concur with that known to Hashem, he may take comfort in the statement of our sages: "Both these and those are the words of our Living Lord" [Eruvin 13a]. If he makes his decision with due diligence, he will be rewarded for his efforts even though he has not divined the real truth.

15טו

Rabbi Bradley Shavit Artson, Everyday Torah, pages 200-201 (2008)

What Is the Authority of the Torah?
Each Sunday morning, some TV preachers hold up Bibles and presume that ultimate authority can be lifted straight out of that book. They argue that the Bible says it, so that settles it. Many Jews have adopted that same approach, insisting that “Torah” Judaism is one in which the Torah has the final word—specifically that the p’shat is final. Thus, anyone who acts against the p’shat of the Torah is violating the will of God and going against the teachings of Judaism.

Yet that assessment of how we should live the Torah is really an act of assimilation, taking on the standards of one type of Christianity as though it were all of traditional Judaism. In reality, Judaism has always insisted that the Torah means what the rabbinic sages say it means and that the p’shat may be interesting from the perspective of study and scholarship (that is, to find out what the Torah meant in its ancient Near Eastern context), but the p’shat is virtually irrelevant to what the Torah means for us today. For that relevance, we have always turned to the drash—the Torah as it is read by each generation of Jews. Not only is that nonfundamentalist Judaism traditional, it is a necessary implication of a belief in Torah sheh be-al peh (an oral teaching that parallels, elucidates, and implements the written teaching). The written Torah means what the oral Torah understands it to mean.

One need not look far for examples in rabbinic writings. The Torah specifies that one cannot exempt oneself from a vow, yet the rabbis disregard the p’shat of the Torah to allow for rabbinic annulment of unwise vows. The Torah specifies the death penalty for certain L e v i t i c u s 201 crimes, but rabbinic interpretation virtually reads capital punishment out of existence—in disregard of the biblical view. The Torah prohibits touching the corpse of an animal that is tamei, yet Jewish law permits it. These are not acts of rebellion, but an assertion that the Torah “is not in heaven”; it is ours to interpret and align with the moral insights of each age. It is a way of continuing to hear the voice of the living God through its words.