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I think this is he:
Gille Míchéil, Earl of Fife:
https://en.wikipedia.org/wiki/Gille_M%C3%ADch%C3%A9il,_Earl_of_Fife
Mormaer Gille Míchéil, (d bef Jul 1136) is the second man we know for certain to have been Mormaer of Fife from 1130 to 1133, although it is unlikely he actually was the second. He had at least one son, called Aed (=Hugo). Aed would have succeeded Donnchad I under a Celtic system, but as feudal rules of primogeniture came into force during the reign of Donnchad I, it was Donnchad's son, and not Gille Míchéil's, who became the next mormaer. Aed, though, probably succeeded to the leadership of Clann Duib, at least during Donnchad I's minority, and certainly became lay abbot of the monastery of Abernethy, an office which his own son, Orm, later inherited.
Also mentioned in the entry for the first Mormaer of Fife: Causantín, Earl of Fife:
https://en.wikipedia.org/wiki/Causant%C3%ADn,_Earl_of_Fife:
...Causantín appears in a charter of King David's, dated 1126, giving confirmation of the rights of Dunfermline Priory and promoting it to Abbey status. His name occurs as a witness, alongside bishops.... as well as his kinsman, Gille Míchéil, chief of Clann meic Duib and others.[11]...
He appears to have been dead by 1130, when another member of the Mac Duib kindred, the Gille Míchéil who appeared alongside Causantín in the charter of 1126, is ruling as mormaer; although the latter may have been using the title comes (mormaer) as early as 1126, and had been using the style Mac Duib since at least 1126.[13] Donnchad I, who succeeded Gille Mícheil, may have been Causantín's son.[14]
[11] ^ see Registrum de Dunfermelyn, (Bannatyne Club, 1842), pp. 3–4; Richard Oram, David: The King Who Made Scotland, (Gloucestershire, 2004), p. 82.
[13] ^ John Bannerman (1993), "MacDuff of Fife," in A. Grant & K. Stringer (eds.) Medieval Scotland: Crown, Lordship and Community, Essays Presented to G.W.S. Barrow, (Edinburgh, 1993), pp. 20–38p. 31.
[14] ^ Bannerman (1993), p. 33.
Aed (Aedh, Aodh, Heth) was a popular name all over the Celtic world. It means "fire", and has been customarily anglicized as "Hugh" despite that name having a completely different derivation and meaning (Germanic "hug", meaning "heart, mind, spirit"). The form and sound was apparently all that mattered. Variations included Aedach/Aodhach, Aedan/Aidan/Aodhan, Aedgal/Aodhal, Aedgen/Aoidhgean, Aeducan/Aodhagan/Egan, and so forth. (Taken from Donnchadh O Corrain & Fidelma Maguire, "Irish Names".)
So, what evidence is there that Gille Míchéil MacDuff, Earl of Fife - is the son of Aed and Lulach's daughter?
Gillemicheil (Gilla Micheil, and other variant spellings) is known to have held the title "Earl of Fife" circa 1120s-1136, and to have styled himself "macDuff" at least once during the same period.
Whether this means his father was someone named Duff (or some reasonable variant thereof), or whether he was an early user of the form "descendant of", is obscure.
His predecessor as Earl of Fife was one Constantine (or Causantin), who was also styled "filius Magduffe" - on a charter that was probably a later reconstruction/forgery.
A "Mackduffe, Comes" is found on another highly suspect charter (King Edgar to Durham, "1095", Lawrie XV pp. 12-13). If we had a better idea when *that* one really dates from (1095 was two years before Edgar was actually crowned,and before then he was just one of several claimants), we might have a handle on how long the "Macduff, Thane of Fife" story had been in existence.
Note: a recent diplomatist (student of ancient documents), A.A.M. Duncan, Emeritus Professor of Scottish History and Literature at the University of Glasgow, argued strongly (in 1958 and again in 1999) for the authenticity of the "Edgar 1095" charter. If he's right, the implications are...interesting.