I am aware that certain scholars either do not take a decided stand on this issue or they suggest that the Greek of the LXX is not (strictly speaking) Koine. The 1905 work by F.C. Conybeare and St. George Stock entitled Grammar of Septuagint Greek states:
"The New Testament, having itself been written in Greek, is not so saturated with Hebrew as the Septuagint: still the resemblance in this respect is close enough to warrant the two being classed together under the title of Biblical Greek" (page 22).
However, A. T. Robertson argues more fervently that the Greek of the LXX is the ancient vernacular of Alexandria. The papyrological corpus seems to favor Robertson's thesis: there is no such animal as "Biblical Greek" (sensu stricto)
This point really should not surprise us since the Koine period evidently lasted ca. 330 BCE-330 CE. During his brief but glorious life, we know that Alexander the Great sought to make Koine a Weltsprache or lingua franca of the ancient world and his desire came to fruition. Why would the LXX have been an exception to this rule? One of the best ways to decide the issue is to compare the LXX with the Greek papyri. One can then see similarities and differences between the two.
Robertson (A Grammar of the GNT) quotes Deissmann concerning the issue of the NT and Koine Greek as follows:
"If we are ever in this matter to reach certainty at all, then it is the inscriptions and papyri which will give us the nearest approximation to the truth" (Deissmann qt. in Robertson, p. 79).
Deissmann continues to build his case by noting that both the LXX and the NT, based on a study of Greek papyri and inscriptions, were translated using "the Greek of ordinary intercourse as spoken in countries bordering on the Mediterranean" and he also observes that this developing common tongue of the Meditteranean people differed in "many respects" from the classical Attic of antiquity (See ibid., pp. 79-80).
As J.H. Moulton concludes in his NT Greek grammar:
"The papyri exhibit in their writers a variety of literary education even wider than that observable in the NT, and we can match each sacred author with documents that in respect of Greek stand on about the same plane. The conclusion is that 'Biblical' Greek, except where it is translation Greek, was simply the vernacular of daily life . . . The NT writers had little idea that they were writing literature. The Holy Ghost spoke absolutely in the language of the people as we might surely have expected He would" (p. 5).