David Kelley states, [1]
The purpose of this paper is to give the known ancestry of Eve of Leinster, the wife of Richard de Clare, Earl of Pembroke, as fully as possibel, omitting only certain problem areas wehich require special study. …
By far the most important primary source of Eve's ancestry is the Ban-Shenchus, a compilation of genealogical information concerning the women of Ireland from the earliest mythical times to the date of compilation. The earliest version was apparently compiled about 1030 A.D., and additons were made in the twelfthe century to bring it up to date. One of these later versions was apparently compiled in Leinster between 1171 and 1175, just after the marriage of the Earl to Eve and during their lifetiems. …
Eve ("Aife, wife if the Earl" in Ban-Shenchus), was the daughter of Diarmait MacMurchada, King of Laigin (usually called Dermot MacMurrough, King of Leister, in English accounts). Like most of these rulers, Diarmait had several wives, the mother of Aife being Mor, daughter of Muirchertach Ua Tuathail (O'Toole) and half-sister of Lorcan ("St. Lawrence O'Toole"), archbishop of Dublin, 1132-80, and the leading churchman of Ireland at this time, according to the same source. The Book of Leinster, written at Diarmait's court during his lifetime, does not mention Mor's mother but otherwise verifies this account …
[1] David H. Kelley, "The Ancestry of Eve of Leinster," The Genealogist Vol. 1, no. 1 (1980), 4-27 at 4-5, [AmericanAncestors].