The Macaulays of Lewis are generally held to be of Norse descent, from an eponymous Olafr. Here’s Rev W Matheson on the subject, from his Families of Lewis series of the 1950s:
Most West Highland clans have to go back some seven hundred years to find their eponymous ancestor. If the Macaulays of Lewis conform to this pattern, we should look for the original Olafr or Aulay about the beginning of the thirteenth century, when the Hebrides were still under Norse domination; and it is a fact, as we know from the Chronicle of Man, that one so called had close connections with Lewis at that time – no less a person than Olaf the Black, who in later years was to become King of Man and the Isles. It is not therefore surprising that Dr George Mackenzie who was doubtless acquainted with the Chronicle of Man as abridged by Camden, makes Olaf the ancestor of the clan.
It is possible that Olaf the Black left descendants in Lewis, but there is no real evidence on the point. There was a tradition among the Macaulays in Uig that they were descended from Magnus, King of Norway, while in Lord Macaulay’s [Thomas Babington Macaulay, 1800-1859, historian and politician] family a similar tradition gave the name as “Olaus Magnus, King of Norway”. The occurrence of the name Magnus may be of significance, for Olaf the Black did, in fact, have a son so called.
He goes on to discuss the name Sgaire, which is peculiar to the Macaulays and which evidently arrived in the family with “Iskair Macaulay ane Irish man” before being anglicised as Zachary, but see below for a fresh interpretation of the subject. There’s probably a good argument for a Macaulay DNA project here.
Thanks to Brianann for this.