Etruscan, on the other hand, was a non-Indo-European language, which had no surviving relatives in Asia Minor in the era of Dionysius of Halicarnassus, at least none that we know of. Its only close relative is the language which was spoken on Lemnos before the Greek conquest--how the Lemnian language was so similar to Etruscan is a difficult thing to explain for those who think Etruscan was indigenous to Italy. In Greek tradition the earlier inhabitants of Lemnos were "Pelasgians." Who the Pelasgians were is not clearly understood--there have been lots of theories, including that they were the same as the Philistines (who seem to have come from the Aegean before settling in historic Philistia).
Etruscan is not related to the other langauges of Italy. Usually when you have a situation like that (e.g. the case of Basque) it's because a language happened to survive in a mountainous or inaccessible area--but the Etruscan language is found in one of the most desirable areas of Italy, the kind of place an invading group might have conquered.
Italian scholars have tended to favor the theory that Etruscan was indigenous to Italy rather than brought in from the east.
Right. Etruscan may have a connection with Rhaetic in the Alps, but that’s not quite established, and the only sure connection is Lemnian, as you mention. I did a little amateur’s analysis on the Lemnian stele years ago, with Bonfante’s Etruscan grammar in hand.
There is really not that much difference at all between the two idioms...they look to me like two slightly different dialects. From what I could see, they didn’t look like languages that had been separated for thousands of years—which sort of puts a crimp in the idea that they represent a pre-Indo-European substrate. Impressionistically, I’d say that the separation between them looks to be only on the order of 500 years or so.
And your point about the languages retreating to the hills and inaccessible areas is certainly well-taken. That’s exactly what happened to Oscan, as the Samnites were deprived of the coasts by Greeks and later Romans.
If the Etruscan parent population had died out by the time of Dionysius, that would explain why he didn’t see any connection. I’m pretty sure Lemnos already lost their language several hundred years prior to his time.