Which name came first, Lucius or Λουκᾶς?

The etymology of the name Luke is commonly said to be the Latin name Lucas, itself from Lucius, from the praenomen Lucius, from the root Lux (gen. Lucis).

[A separate etymology says Λουκᾶς/Λουκανός, derived from a term meaning "man from Lucania". But I’m not particularly concerned with that supposed etymology in this question]

Elsewhere (reading about Leucism in biology (white stag)) I came across the Geek word λευκός(HGL) and wondered if that was not a more suitable or a cognate etymology, and found the Greek name Loukâs ‎(Λουκᾶς) said to be derived from it.

Both Lux and Leukos have the same Proto-IndoEuropean etymology of *leuk-, meaning "bright", "to shine", "to see".

In De Praenominibus (Concerning Praenomina), Julius Paris asserts that Lucius is derived from lux, light, and that the name was originally given to children who were born at dawn. 

Can anyone discover or deduct from historical records what came first: the Latin Lucius from Lux, or the Greek Λουκᾶς from Λευκός? Indeed, perhaps there was a PIE name *Leukos which predates them both! Perhaps an Etruscan or Umbrian origin that someone can find?

Update: … identifiable Umbrian elements in the Etruscan language. … An Umbrian rather than a non-specific Italic origin can be fully demonstrated only when the form in question shows characteristic Umbrian sound-changes. … specifically Umbrian are the names vuvzies, vuσia < *Loukios, *Loukiā with Umbrian palatalisation of Italic *k before a front vowel and change of initial *l- to v- (whereas luvce, lauci etc. are borrowed from Latin (cf. class. Lūcius)).

Continues: The complexity of loan relations may further be illustrated by lauχme, lauχumes (a personal name with a derived gentilicium lauχmsni etc.) and lucumu as a cognomen: are these to be linked with Lat. Lucumō, a personal name but, according to Servius, originally the Etruscan word for ‘king’? Does lauχumneti in the text of the linen book (LL IX f2) belong here as ‘in the regia’ (Meiser 1996, 195)?

An Italic origin, from the root *leuk- shine’ has often been suggested (most recently by Meiser apud Rix 2005, 564 fn.12, starting from Umbrian *loukumō ‘the most brilliant’); Agostiniani (2003) wonders if there might rather be a connection with Italic *loukos ‘sacred grove’, but notes that in either case the -χ- is unexpected. Can any safe conclusion be drawn?

Source: Defining the Etruscans: Language and DNA, John Penney