M.Sjostrom at SGM says Gruaidh was "was almost certainly either daughter or sister of king Aonghus mac inghen Lulaich." He also lists other members of this family.
https://groups.google.com/forum/?hl=en#!topicsearchin/soc.genealogy...
Sjostrom links to Leo Van De Pas at Genealogics, but Geologics says only that Gruaidh was daughter of Aedh / Heth (citing Paget).
http://genealogics.org/getperson.php?personID=I00076167&tree=LEO
Roger of Howden had also heard about the MacWilliam expedition of 1187 and it is from his account that speculation has arisen regarding a marriage between William fitz Duncan and a female relative of Oengus of Moray:
Interim Willelmus rex Scotiae, magno congregato exercitu, profectus est Moraviam, ad debellandum quendam hostem suum qui nominabatur Mach Willam: qui etiam dicebat se regia stirpe genitum, et de jure parentum suorum, ut asserebat, regnum Scotiae calumniabatur,
et multa et incommoda faciebat saepe Willelmo regi Scotiae, per consensum et consilium comitum et baronum regni Scotiae.
(Meanwhile William, king of Scotland, collected a great army, and set out for Moray, to subdue a certain enemy of his, who was named MacWilliam; who also said that he was born of the royal stock, and by right of his parents, so he affirmed, claimed the kingdom of Scotland, and often did many and harmful things to William, king of Scotland, through consent and council of the earls and barons of the kingdom of Scotland.)30
In this passage Roger of Howden stated that Donald bán claimed the kingdom of Scotia in right of his parentes. This statement, which is almost certainly accurate given the time that the author spent in
Scotia towards the end of the twelfth century, has been taken to mean that the mother Donald bán was important in her own right. As we have already seen Barrow suggested that this woman was either a cousin or sister of Oengus of Moray.31 Oram further developed this theory in 1999 and noted that as a descendant of King Lulach mac Gilla Comgáin, Donald bán would have inherited membership of theroyal kindred of Clann Custantín meic Cináeda. Furthermore, Oram argued that the marriage o William fitz Duncan to a Moravian woman may have been deliberately encouraged by King David I as a means of 'tying-off' the claims of two collateral branches of the royal kindred, although such a
calculation was predicated on the gamble that any children of such a union would be uninterested in pursuing their own claims.32 To a large extent this theory depends on the belief that Donald bán actually received support from Moray between 1179 and 1186. As we can see, there is not a shred of evidence to suggest that this was the case. Accordingly, William fitz Duncan's first marriage could have been to any female member of the royal kindred. More importantly perhaps, the theory that the mother of Donald bán was closely related to Oengus of Moray depends on translating the Latin word parentes as 'parents', rather than 'ancestors' or 'kindred'. The use of either of these latter two meanings suggests that there need be no parental link between Donald bán and an important Moravian woman. In fact, this word may simply
refer to his paternal descent from King Donnchad mac Máel Coluim and the fact that he belonged to the royal kindred.33
Notes:
30 Stubbs, Gesta Regis Henrici, ii, 7-9.
31 RRS, ii, 13.
32 Richard D. Oram, „David I and the Scottish Conquest and Colonisation of Moray‟, in Northern Scotland, 19,
1999, 1-19, at 10.
33 To date only A.A.M. Duncan seems to have translated parentes as 'kin', [cf: Duncan, 'Roger of Howden', p.141]
Ross, Alasdair (2007), "Moray, Ulster and the MacWilliams", in Duffy, Séan, The World of the Galloglass: Kings, Warlords and Warriors in Ireland and Scotland, 1200–1600, Dublin: Four Courts Press, ISBN 978-1-85182-946-0
https://dspace.stir.ac.uk/bitstream/1893/2174/1/Moray,%20Ulster%20a...