ETR001 is Roman, not Etruscan. In all the PCAs she is in the opposite side of Greeks, but that she may have partial Greek origins is possible, but this has nothing to do with the origins of the Etruscans that in the PCAs are positioned far from the Greeks and join the south-western European cluster. Lemnos was conquered by the Athenians and became Greek in all respects. I have read all of the most recent SAIA studies, Italian Archaeological School of Athens, and they have found no evidence that Lemnos is related to the origins of the Etruscans. On the contrary, the hypothesis that is considered most credible is that there were small groups of Etruscans from Cerveteri on the island.
The Greeks have never had colonies in Etruria but their presence is attested, the Greeks are among the main interlocutors of the Etruscans and therefore they were not certainly few. But above all it depends on the zones of the Etruria and by which kind of Greeks. The Syracusan Greeks were considered almost always enemies, with the Foceian/Ionian Greeks very unstable relations, and with the Athenians there were often good relations. At Delphi in Greece the Etruscans brought gifts. In Tarquinia, southern Etruria (northern Lazio), for example, must have lived a Greek community from Ionia (Anatolia) around 600-500 BC that will not have been very small numerically. But if the shift occurred in the imperial era it is no longer something that depends on the Etruscans, but on the Romans. According to archeology in the settlements in Campania, southern Italy, the Etruscans were most likley very mixed with the Greeks and the sorrounding local populations.