Judaism does not consider the Septuagint as inspired or as canon. If early Gentile Christians used it out of necessity it is still clear the New Testament writers did not always use it verbatim. In that sense they also agree it should not be treated as "inspired."
The LXX does have a role to understanding the OT as it reflects how Hebrew scholars interpreted the original (unpointed) Hebrew and, as the LXX was done before Christ, has no Christian basis. A good example is Isaiah 7:14 where the literal Hebrew העלמה means "the young woman" yet is almost always translated as "virgin" in Christian Bibles. However, "virgin" (παρθένος not παιδίσκη) is also how the LXX translator(s) interpreted the text. That is, Hebrew scholars, before the Christian-era understood the original text spoke of a young woman who was a virgin giving birth to a son. Obviously, the New Testament writers record an "inspired translation" which in this instance agrees with the LXX.
When the OT is cited in the NT the Greek as is essentially an inspired translation (which may or may not agree with the LXX) and, as is the case with the New Testament treatment of the Old in general, may include additional revelation which will explicate the Hebrew text.
The passage in Luke is not Jesus quoting the Old Testament:
25 And behold, a lawyer stood up to put him to the test, saying, “Teacher, what shall I do to inherit eternal life?” 26 He said to him, “What is written in the Law? How do you read it?” 27 And he answered... (Luke 10) [ESV]
"Lawyer" is νομικός, which in the NT is used of an interpreter and teacher of the Mosaic Law. Essentially his answer is like the work of the scholars who translated the LXX in that it demonstrates his interpretation of the Mosaic Law (which in this case Jesus approves). The lawyer pieced together a passage in Leviticus (19:18) with that of Deuteronomy. Here is the portion from Deuteronomy in question:
You shall love the LORD your God with all your heart and with all your soul and with all your might. (Deuteronomy 6:5)
ואהבת את יהוה אלהיך בכל־לבבך ובכל־נפשך ובכל־מאדך
You shall love the Lord your God with the whole of your mind, and with the whole of your soul and with the whole of your power. (LXX-Deuteronomy 6:5)
καὶ ἀγαπήσεις κύριον τὸν θεόν σου ἐξ ὅλης τῆς καρδίας σου καὶ ἐξ ὅλης τῆς ψυχῆς σου καὶ ἐξ ὅλης τῆς δυνάμεώς σου
And he answered, “You shall love the Lord your God with all your heart and with all your soul and with all your strength and with all your mind, and your neighbor as yourself.” (Luke 10:27)
ὁ δὲ ἀποκριθεὶς εἶπεν ἀγαπήσεις κύριον τὸν θεόν σου ἐξ ὅλης τῆς καρδίας σου καὶ ἐν ὅλῃ τῇ ψυχῇ σου καὶ ἐν ὅλῃ τῇ ἰσχύϊ σου καὶ ἐν ὅλῃ τῇ διανοίᾳ σου καὶ τὸν πλησίον σου ὡς σεαυτόν
The lawyer did not quote either the LXX or the Hebrew:
Two points: (1) Both the Hebrew לֵבָב and Greek καρδία mean "heart" but can be interpreted as "mind." (2) Where the LXX translator chose to translate מאד as one word, δύναμις (force), the lawyer used two words ἰσχύς and διάνοια (strength and mind).
The first thing to note about the lawyer's treatment is that it makes specific what is implied in either the Hebrew or LXX. Namely, love with all of your "לֵבָב" or "καρδία" means both the heart and the mind. However, the lawyer accomplished this by placing mind (διάνοια) at the end of the passage which also has the effect of interpreting the Hebrew "might" (מְאֹד) as "strength and mind."
This is a better interpretation into Greek than the LXX since the meaning of the Hebrew מְאֹד, here is unusual as Bernard M. Levinson explains:
Might: Hebrew "me'od" is elsewhere an adverb meaning "very" or "exceedingly." It is used as a noun only here and in the Deuteronomistic description of King Josiah, which cites this verse in order to portray Josiah as the paragon of obedience to Torah (2 Kings 23.25). While the word's basic meaning is "might" or "strength," it was understood as "wealth" or "property" both at Qumran (CD 9.11; 12.10) and in early rabbinic literature (Tg. Jon.; Sifre). The two interpretations each call for full commitment to God, whether psychology or practical; both are preserved in the Mishnah (m. Ber. 9.5).
Arguably the lawyer rejected all other interpretations of the period (LXX "force;" Qumran/rabbinic "wealth" or "property"), and understands the Hebrew "me'od" to meaning a person's entire strength and mind.
Neither Judaism nor Christianity disputes the lawyer's assertion that Deuteronomy 6:5 should be taught to include loving with all of the mind. Therefore the passage in Luke does not reflect corrupted texts or the influence of Hellenism. Rather, it demonstrates the teachers of Law were able to succintly explain the Mosaic Law using the Greek language:
And he said to him, “You have answered correctly; do this, and you will live.” (Luke 10:28)
The passage in Luke shows how a Jewish scholar of the period used the Greek language to summarize the Law. His interpretation was novel in that it did not follow the LXX, or the Qumran, or the rabbinic interpretations.
1. Bernard M. Levinson, The Jewish Study Bible, Edited by Adele Berlin and Marc Zvi Brettler, Oxford University Press, 2004, p. 380