Tressa recently posted a solid introduction to the scholarly information on Lugh, which saves me the trouble of doing the same. I wanted to add a few notes, particularly on names and etymologies.
The etymology of Lugus/Lugh is contested, but there seems to be some consensus among English language articles that the most likely root is *leugʰ-“to swear an oath” (Koch 1992; Wagner 1970). Several of the French language articles I’ve been able to access still prefer to the *leuk-“to shine” etymology, arguing the linguistic shift could easily have occurred post the IE to Celtic transition and that the relationship is clear in Brythonic Celtic words rooted in*leugʰ- (Hily, 2007; Bader 1989). Jordan Cólera (2005) argues both are correct, as both contributed to the formation of the name.
But what I find more interesting than the linguistic root arguments are the punning relationships that are less about the denotation of his name and more about the connotations to native speakers. In some of the medieval Irish texts, Lug and Lugaid are used interchangeably (Grey 1989). More than one author has noted that Lugaid easily puns with luchaid, “mouse” (Koch 1999, Coe 2005). This may explain a strange incident in the Cath Maige Mucrama where Lugaid Mac Con is outed as the leader of his warrior band when they are served mice for dinner by a foreign king, as any Lugaid would likely be unable to eat mice, just as Cú Chulainn had a geas against eating dogs (Koch 1999). This punning also offers an interesting connection between the winner of the harvest story of Lug (Mac Neil 1945) and the fourth branch of the Mabinogi where Manawydan must defeat a troublesome mouse-king, Llwd (grey), to save his ensorcelled land and people (Koch 1999; Coe 2005).
In folktale versions of Lugh’s birth, he is often called Lui Lavada, and his name is said to have been, like Welsh Lleu, won from an unwilling relative, in Lugh’s case, his grandfather Balor. Cian–Kane or McIneely in many folk versions–is working as Balor’s gardener and drops a basket of apples. As everyone hurries to gather them, the yet-unnamed child Lugh manages to pick up more than anyone. Balor exclaims over the “little long arm,” Lui Lavada, and thus gives him his name (Varin 1979; Krapple 1936). This shows another punning relationship with the name, as Lugh sounds like lú, something small or of little value (eDIL), in Irish. In folktales, this often lends him the character of the Jack the Lad character–small, underestimated, yet ultimately victorious, the archetypal underdog who defeats the bullies.
A third pun on the name is lug “lynx,” a word also used to metaphorically mean “warrior” in the early literature (Hily 2007; Maier 1996). I haven’t seen much argument for the use of this pun, however–more often, as in Maier, this is used as an argument that some translations suggested to reference Lugh are really just talking about the lynx, especially regarding names of people and places.
What I find fascinating about all this is the way playing with language (and so far as I can see, Irish speakers love to play with their language) can expand our understanding or widen our vision for possibilities of who Lugh is. As Tressa says, he is a complicated and many-faceted god.
References not linked above
Bader, F. (1989) La Langue des dieux ou l’hermétisme des poètes indo-européens, Pise, Giardini (Testi Linguistici n° 14).
Cólera, J.(2005) “Crónica de un teicidio anunciado”, Estudios de Lenguas y Epigrafia Antiguas, VII, 37-72.
Wagner, H. (1970) ‘Studies in the origins of early Celtic Civilisation’, ZCP 31: 22, 24-25, notes 27-29, et passim.