I would like to express an opinion regarding Herodotus and his version on the Etrucan origins. Despite his theory on a anatolian - and specifically lidian - origin of the etruscans has been pretty much disprooved both by archeological and genetic analysis, I think we might consider it as some sort of collective memory of actual contacts between the early etruscan/tyrsenian world and the lidian/anatolic context in the late bronze age, maybe during the so called bronze age collapse.
We know that many peoples around this time were indeed active as pirate, mercenaries and adventurers in the eastern mediterranean. Some of this peoples have been linked to the mycenaean world, other to the italic one. Its therefore possible that during the late bronze age and the early iron age mercenaries and pirates from the tyrsenian world were operating in the Aegean Sea, maybe hired by some mycenaean or lidian king. We do know that the etruscans were actually active in the aegean context in the Iron age, at least on isalnd of Lemnos.
So, maybe, the fabled and now disproved anatolian origin of the etruscans could actually be interpreted as a mere memory of contacts between this two worlds.
Of course, this is just an hypothesis, but it could conciliate the autoctonous origin of the etruscans with the account of Erodotus.
I have never read of archaeological evidence of contacts between the Proto-Etruscan and Lydian worlds during the Late Bronze Age, let alone migrations. As Etruscologists have been explaining for years, it was the archaeologists of Prehistory and Protohistory, after more than 40 years of excavations, who concluded that there are no archaeological traces of migrations to Etruria who may support the Greek accounts (Etruscologists deal mainly with the Iron Age, for obvious reasons). Trying to give credence to Herodotus' account, as Enrico Benelli recently wrote, is like claiming that the earth is flat.
Only in the pseudoscientific world the Greek accounts on the Etruscans have remained popular (which are based on two separate traditions that arose separately and many centuries after the ethnogenesis of the Etruscans), and in non-specialist studies on the Etruscan world (e.g. in some Indo-European linguists). For various reasons. Not least the fact that the Etruscans have been instrumentalised for years by any nationalistic claims.
The contacts are between the Etruscans and the Greek Ionian world, and it is within this world that this invented tradition was born. Like the other, the Pelasgian one, which probably originated in Athens. As scholars of these topics have explained many times (in the forums no one reads but everyone has an opinion),
Greek authors speak to themselves first. By the Lydian origin and the Pelasgian origin, the Greeks mean that the Etruscans are somehow connected to the Greek world, albeit in a peripheral way (it is the Greeks who are connected to the Pelasgians and the Lydians). When Dionysius of Halicarnassus lives, the relationship between the Etruscans and the Greeks has changed. The Greeks now have an interest in tying themselves to the Romans, and no longer to the Etruscans (an interest shared by the Romans themselves, who want to ennoble themselves). So, the Etruscans finally become autochthonous, and according to Dionysius it is the Romans who are of Greek origin.
The theme of origins in Greek authors always reflects a Greek point of view, it should not be interpreted as if they were history and anthropology books written today. But Dionysius' account finally also contains information that turned out to be true, including even the name used by the Etruscans themselves.
The first Greek source to mention the Tyrrhenians is Hesiod, many centuries before Herodotus. Hesiod makes no mention of an eastern origin of the Tyrrhenians and places them exactly in central Italy close to the Latins. There is no other ancient source before Herodotus that associates the Tyrrhenians with the Lydians. Also for the Herodotus' story, the Tyrrhenians are those who are in Italy, not in Lydia.
As reported by Dionysius, Xantos of Lydia, the historian considered the highest authority in the history of the Lydians, makes no mention of Tyrrhenus as son of Atis, or of a Lydian colonization in Italy. As many scholars have pointed out, the Herodotus' story is based on false etymologies. It is likely not Herodotus' fault, since he reports what others had said.
In fact, according to Xantos of Lydia, Atis' sons were Lydus and Torebus and they, "having divided the kingdom they had inherited from their father, both remained in Asia, and from them the nations over which they reigned. (...)
"From Lydus are sprung the Lydians, and from Torebus the Torebians. There is little difference in their language and even now each nation scoffs at many words used by the other, even as do the Ionians and Dorians."
By mistake, deliberately,
Torebus and the Torebians have become Tyrrhenus and the Tyrrhenians. But Torebus and the Torebians were clearly not Tyrrhenus and the Tyrrhenians. This is where the Lydia origin story starts, from a linguistic manipulation.
Xantos of Lydia reported by Dionysius:
"But Xanthus of Lydia, who was as well acquainted with ancient history as any man and who may be regarded as an authority second to none on the history of his own country, neither names Tyrrhenus in any part of his history as a ruler of the Lydians nor knows anything of the landing of a colony of Maeonians in Italy; nor does he make the least mention of Tyrrhenia as a Lydian colony, though he takes notice of several things of less importance. He says that Lydus and Torebus were the sons of Atys; that they, having divided the kingdom they had inherited from their father, both remained in Asia, and from them the nations over which they reigned received their names. His words are these: "From Lydus are sprung the Lydians, and from Torebus the Torebians. There is little difference in their language and even now each nation scoffs at many words used by the other, even as do the Ionians and Dorians."
The origins of the Etruscans have nothing to do with the Greek and Aegean worlds. Unless we want to see a Neolithic connection, but this concerns the whole of Europe, not just the Etruscans. Therefore the story reported by Herodotus would have no value in any case. Even the presence at Lemnos of two inscriptions in a language similar to Etruscan, after 100 excavations, did not yield any clues in favour of Greek accounts. Small groups of Etruscans were indeed around the Mediterranean. Not to mention foreign presences in Etruria, starting with the Ionian Greek painters who were very active in Etruria in the Archaic phase and whose style contributed to further confusion. But this does not change the general picture of their origins. The Etruscans were a people who had many contacts with all those around them, including clearly the Greeks who were the link, together with the Phoenicians, between the eastern and the central and western Mediterranean. Unfortunately, we know nothing about what the Etruscans really thought of the Greeks (and even of the Romans and the others), as only Greek and Latin texts have survived.