The conclusions to his paper are threefold.
Firstly, he affirms and demonstrates that the very common translation for YHWH is kyrios, without the definite article (absence of "the"), and that this strongly implies a consistent grammatical rendering for a name. Although only looking in detail in Exodus, there are still hundreds of samples to work with, and Perkins shows that of the exceptions to the rule (i.e. those times where Kyrios is articulated), it is well within the norms, at approximately 6%. Other names like "Israel", "Moses" etc have similar percentages of articulated translations in the Greek.
Secondly, it is therefore for Greek reasons, not for Hebrew reasons, that the articulation occurs, implying even more consistent intention - I would say anything from 95% to 100% of Kyrios occurrences with reference to YHWH - that Kyrios is a translation of the divine Name, and not a (or the) divine Title when translating Yahweh (there are a few instances - not many - of Adonai in the Pentateuch, that need separate consideration).
Thirdly, Perkins is confident that the original translator of the LXX applied "Kyrios", anarthrously of course. On this third point, however, there seems to be an underlying assumption in Perkins (and possibly some of the other work done in this area - I need to re-check Martin Rosel's benchmark piece) that overstates the translator/copyist distinction. Like Rosel, he covers some of the complicated historical issues. The most critical of these is a lack of explicit textual support for a pre-Christian rendering of Kyrios in the Old Testament, although various explanations can be provided for this, which I may summarise in another post. My view on this is that without further evidence, we need to adopt a more fait accompli approach to this complex translation process, whereby Kyrios, without the article, emerges as a suitable translation for the divine Name. The meaty question remains: why in English and other modern languages is the carefully preserved name converted back to a title? It's an historical question that will take us back at least to the KJV.
FYI: Perkins includes an interesting footnote on the last page of his paper. It reads: "The reasons why the Greek translators of the Hebrew text chose kyrios as the rendering of the divine name remain somewhat unclear. It is quite possible that the use of this term within Egyptian documents to describe the Pharaoh and divine beings gave its use in the Jewish Alexandrian community for YHWH."