Peter Head (Christology and the Synoptic Problem. Cambridge: Cambridge UP, 1997. pp. 160-162) notes:
It now seems unlikely that KURIOS translated YHWH in
pre-Christian versions of the Greek OT. The oldest
[MSS] of the Greek OT, and every [MS] of known [sic]
Jewish milieu, use YHWH in Hebrew letters, sometimes
in Aramaic, sometimes in palaeo-Hebrew.
He then lists P.Fouad 266 (2nd cent. BCE); 8HevXIIgr (1st cent. BCE); 4QLevb which employs the form IAW; the Cairo Geniza fragments of Aquila, Symmachus and P.Oxy.1007 (Head, p. 161).
After listing evidence for this conclusion from the ANF, Head then cites Jellicoe's "The Septuagint and Modern Study." This work evidently states that KURIOS as a replacement for YHWH "was a Christian innovation." However, Head thinks that the observation by Jellicoe and similar comments made by George Howard must be "nuanced somewhat" since Philo and Josephus apparently employed KURIOS and QEOS to render YHWH. See Philo, De mutatione nominum 18-24 and Josephus, Antiquities XIII.68; XX.90. But the latter author begins writing and comes after Christianity began.
Head thus concludes that Greek-speaking Jews were in the habit of pronouncing KURIOS and allegedly substituting this Greek term for YHWH in theological discussions and in their sacred texts. Head further appeals to the literature from Qumran (1QapGen) to prove that some Jews substituted "other forms" for YHWH, though I do not think this specific point makes his argument more robust, since the Qumran example that Head provides is apparently not a case of YHWH being replaced by KURIOS; nor does a similar quote from Origen (Psalms II.2) help because Origen just says that the Greeks pronounce ADONAI as KURIOS.
The rest of his discussion merits attention too.