Lars (or Lar in some texts) was the Latin spelling of the Etruscan name Larth (larθ). Similar-sounding Etruscan names, like Laris, may also have been spelled Lars in Latin. Some bilingual speakers of Etruscan and Latin, however, used the name Lucius in Latin and Larth in Etruscan, instead of simply transliterating Larth as Lars. (We know this from multilingual inscriptions.) It was a praenomen (forename) and had a feminine form, Larthi, and it was the origin of the Latin nomen (family name) Lartius.

The Lewis and Short Latin dictionary suggests that Lars was “an honorary appellation in Etruscan, = Engl. lord”. As far as I can tell, books by scholars of the Etruscan language do not take it that way, they consider it to be simply a personal name. There are a couple reasons for this. First, in the onomastic formulas in Etruscan inscriptions it behaves like a name, not like a title. Second, “Larth” was quite a common name, not restricted to rulers. It appears in many different inscriptions, including as the name of enslaved and formerly enslaved people. It is also not in the Etruscan names of all rulers; for example, the bilingual Etruscan-Punic Pyrgi tablets refer to Thefarie Velianas, king of the Etruscan city of Caere, who does not have this name. (His praenomen Thefarie is the equivalent of the Latin praenomen Tiberius.)

What that interpretation gets right is that it was a name of several Etruscan rulers. This was likely because it was the name traditionally given to the elder son in Etruscan families, while the younger son was called Arnth (spelled Arruns in Latin). The semi-legendary Latin histories of the Etruscan kings of Rome show this pattern (for example: Demaratus had two sons, the older Lucius and the younger Arruns; that Arruns had two sons, Lucius and Arruns, Lucius Tarquinius Superbus had a younger brother named Arruns), as does an inscription dedicated by two brothers named Arnth and Larth Velimnas.

The Latin Liber de Praenominibus ("Book on forename”s, a treatise of unknown date and author) says that "the forename of Lars was taken from the Lares, but believed to be Tuscan," the Lares being spirits in Roman religion. Etymologies in classical texts should not be taken as authoritative; it could be true, but the Romans did not actually know the etymologies of names, and lots of things in these kinds of treatises are false.

Select Bibliography

Wallace, R 2008. Zikh Rasna: A Manual of the Etruscan Language and Inscriptions

Bonfante, G and Bonfante, L, 2002. The Etruscan Language: An Introduction, Revised Edition

Farney, G 2010. "The Name-Changes of Legendary Romans and the Etruscan-Latin Bilingual Inscriptions: Strategies for Romanization." Etruscan Studies 13(1)

EDIT: I have made edits to this; see the discussion below for more information.

I can't give you a great answer, but here's some info you may find useful, or that you may find to obfuscate:

First of all, the Etruscan language is not by any means fully deciphered. There are several reasons for this, including that it clearly isn't an Indo-European language and appears unrelated to any modern languages, the closest analogue languages are also extinct*, and ancient treatises on the language (most famously by the Roman emperor Claudius) are lost to us. All these things make the Etruscan language uniquely difficult for modern researchers to decipher. Some of the language is, indeed, known, though I don't think there's a complete modern explication of the Etruscan language.

Secondly, Lars is a name that appeared to have variant forms in antiquity, like "Lar", "Larth," "Laris," and others. So unfortunately, I don't really have an answer to your question barring recent research.

I'm going into conjecture here, so I'll ask a follow-up question to any and all historians and/or linguists here: Is there an etymological relationship between the Etruscan name "Lars" and its variants and the Roman term "lar, laris" for a household deity/warding spirit/something?

*I've heard of connections to extinct Alpine languages and to languages from Greek islands, notably Lemnos, though I haven't the skills or background to comment on these potential connections.