My philosophy is that thought is never done and conclusions are often temporary. This is how adaptive learning works. So I continue to revisit things, always looking for a better answer. That Lemnian inscription I previously talked about here and here is still weighing on my head and I just thought of another possible interpretation worth considering.
Previously, I suggested that hktaiunuśi may refer to a personal name and thus 'on behalf of Hektaion'. However I stumbled on another Greek comparison that shows promise: Ἑκάταιον 'temple or statue of Hecate'. Such a loanword would give a different value for hktaiunusi, 'on behalf of/for (-śi) the temple of Hecate (hktaiun-) ', implying that the stone base in question was bearing a statue of the goddess Hecate. Indeed, Hecate was known to be an important deity in Samothrace, right next door. What a nice coincidence. So I could just shoot myself for not piecing this together before.
Keeping with my understanding of heluke as 'has slain' and assuming Suffixaufnahme, the indirect object of the action is *śurum aśil in unmarked form (ergo, a double-marked genitive śurum-s aśl-as). The phrase then must refer specifically to a sacrifice being offered up to Hecate. This might bear fruit considering Aramaic *šōr [šwr] 'ox' and the Greek sacrifices known as hecatombs.
But what then is *aśil? My Etruscan database calls up one instance of exactly this word in TLE 205 although I've been unsure whether it was simply a transliteration error for acil or not. Other Etruscanists seem likewise confused and I have no photo of it. Helmut Rix transcribes the second line as asil sacni and I notice that Paul Kretschmer had once translated it has 'holy altar'. I wonder if this is close to the mark. By giving Etruscan asil the value 'altar', asil sacni becomes 'altar (of the) sacred' and then the Lemnian inscription, Hktaiunuśi heluke śurums aślas, becomes "For the statue of Hekate an ox (or hecatomb?) for the altar has been slain."
 Rice/Stambaugh, Sources for the study of Greek religion (1979), p.161 (see link).