The text traditions, mainly from the Dinsenchas, give Lug four wives: Buí, Nás, Echtach, and Englic*. These four are named in the Metrical Dinsenchas (Gwynn translation):
Echtach, daughter of white-toothed Daig, Englec, Nás, guileless Buí these are the wives of Lug, lord of hosts, who were the flower of gracious queens.
And in an 11th century poem by Flann Mainstrech in the Yellow Book of Lecan:
Echtach, daughter of the Dagda with white smoke, Englic, Nás, Buí, without treachery/cheating, these are the wives of Lug, with many troops.
Various tales of each of them are recorded in the Dinsenchas** but we have no stories of how or why or when Lug married any of them. Some neo-pagan groups have associated Lugnasad with Lug’s marriage to the land—and I’ve seen recons argue that the neo-pagans made this up, but they’re actually in older company.
Lug’s marriage was a topic of interest in the late 19th and early 20th century, with several scholars proposing Lugnasad as being the celebration of his marriage (to someone). The earliest mention of this idea I’ve found is John Rhys in his 1896 Lectures on the Origin and Growth of Religion as Illustrated by Celtic Heathendom, where he suggests that nasad is related to Latin nexus ‘a tying or binding together, a legal obligation’ and that a derivative, ar-nass is used to denote betrothing a daughter. He then goes on to connect this with a quote he had from a book in the library of the Royal Irish Academy D, iv..2:
The Refuse of the Great Feast which I mentioned, that is Taillne. It is here that Lug Scimaig proceeded to make the great feast for Lug mac Ethlenn for his entertainment after the battle of Mag Tured ; for this was his wedding of the kingship, since the Tuatha Dé Danann made the aforesaid Lug king after the death of Nuadaa. As to the place where the refuse was thrown, a great knoll was made of it: this was [thenceforth] its name, the Knoll of the Great Feast, or the Refuse of the Great Banquet, that is to say, Taillne, at the present day.
￼Along with references to Baile in Scal, where Lug is seen with a beautiful woman he names as the Sovereignty of Ireland, Rhys takes this to mean that Lug married the land (the Sovereignty) which he names Eirinn, and that it was this event Lugnasad actually celebrated, rather than the funeral rites of gods who were unlikely to have actually died in truly pagan myths.
This idea was taken up by a number of other early scholars, to the point that it was sometimes mentioned in passing as taken for granted. Westropp (1920) offers this in his “The Marriages of the Gods at the Sanctuary of Tailltiu”:
Oengus, after the so-called ” first battle of Magh Tured,” made the Lugnasad feast for the marriage of Lug to (the kingdom of) Eriu, when Lug was made king after Nuada. One may recall the cryptic allusion in a Gaulish tablet found at Alesia: “May the marriage (?) rejoice the god Ucuetis in Alesia.” Now Eriu was in some tales a daughter of Umor and Tailltiu was daughter of Mac Umoir. The solar god “Mac Greine,” too, had married a goddess (the same, or bearing the same name) Eriu, and was defeated (and “slain”) at Tailltiu by the Milesians. We seem to be hot on the scent of the lost tradition of the goddess who fostered the sun god at the Fir Bolgic sanctuary.
￼Probably the most intensive study of this was done in Grufydd’s Math uab Mathonwy, a study of that branch of the Mabinogion, in which Grufydd searched for the Ur-myth that inspired the Mabinogi of Math. Part of the work he did with this was comparing the tales of Lleu Llaw Gyffes and Lug Lamfada among other Irish stories presumed to be related, to develop this story skeleton:
(I) A certain Giant (or King) had an only daughter. It had been prophesied that his daughter’s son would kill the Giant with a particular spear, on the night of his wedding.
(2) He, therefore, guarded his daughter from all men in a strong tower, so that she should have no son.
(3) The Hero, by magic help, gained access to the Giant’s daughter, and begat a son.
(4) The Giant’s daughter gave birth to a son.
(5) The son did not prosper until he got a name from the Giant, his grandfather.
(6) By magic means, the Hero forced the Giant to name his grandson Lui Lavada/Lleu Llaw Gyffes.
(7) In the circumstances indicated in the prophecy, that is, on his own wedding night, Lui/Lleu hurled the particular spear as described in the prophecy into the Giant’s eye and so slew him.
Whether this is an accurate reconstruction is uncertain, but the amount of material Gruffydd drew on to develop his hypotheses is impressive. This book is dense with stories from both the texts and from recorded folk tales. Unfortunately his story reconstruction does very little to tell us why this story would have been important, giving only structure and not the meaning held in the culture(s) that told it.
Much of this scholarship is denigrated today, often for good reasons: early methods were not terribly rigorous with random suppositions sometimes replacing well-reasoned hypotheses, there was a tendency to try to crush every mythology into cognates of Greek myths, and the idea that more than one person might have the same name was generally ignored in favor of collapsing them into one, among other issues.
Yet no one can deny the tradition of Telltown marriages, and marriage traditions at a variety of Lugnasad sites, as recored by Marie MacNeill in her masterwork on the holiday. Sadly, none of this answers the question of how and when and why Lug married any of the wives we have recorded or whether Lugnasad actually was originally a commemoration of the marriage of Lug to the Sovereignty of Ireland. There is some tie between Lugnasad and marriages—as well as the more often mentioned funerals of women such as Tailtiyu, Buí, Nás, and Carman.
* Spellings of these names vary, but these seem to be the more commonly used spellings. One text mentions Buach, but scholars seem to have effectively argued that this is a variant of Buí (also Bua, Boí).
** Buí: Knowth, Nás; Nás: Nás; Englic: Bansenchas, Knowth (though the relation to Lug is not mentioned here); Echtach alone is not mentioned in these sources, unless there’s another spelling I’m missing.