Weiss attempts to crack it by properly noting the preterite verb at the end. However drawing blanks on precise values, he describes hktaonosi as a possible 'pertinentive' and suspects that soromš : aslaš looks like a subject phrase. The last suggestion must be based on his training in Italic Indo-European languages but this language family won't help him here. Scholars agree that Lemnian is related to Etruscan and entirely non-Indo-European.
To begin deciphering this inscription, we must first transliterate this inscription better. Since we know from the Lemnos Stele that the Lemnian alphabet used omikron for /u/, we should replace o with u. If anything, this helps make the relationship with 'o-less' Etruscan more obvious, aiding in translation. Also the third item, hktaonosi, is surely malformed since we also know from Etruscan study that this is a language with a fixed stress accent on the first syllable. The cluster hk- is quite impossible so this spelling must either be a transliteration error or a scribal misspelling for, presumably, *hektaunusi.
Weiss is correct that the last word is a preterite verb, specifically a perfect preterite which Etruscan marks in -ace. The stem hel- is also comparable to Etruscan where it appears to mean 'to slay, to kill'. This immediately establishes that this sentence refers to an offering being made.
We should analyse hktaunusi as a dative in -si signifying 'for' since this case suffix is found identically in Etruscan. Presumably then, aslaś h[e]ktaunusi is to whom the sacrifice was performed. Judging by other inscriptions of this nature, it's no doubt the name of an individual. This leaves surumś, an apparent type-I genitive in -ś which must be what was sacrificed.
We arrive at a provisional translation of "[Surum] has been slain for Axulos Hektaion." I presume here that the name of the recipient in question is Greek, a conclusion that I doubt would be objectionable considering its context on an Aegean island.