This is from WD Simpson’s ‘Notes on Lulach’s Stone, Kildrummy’ (which is actually another stone of the same name):
On Green Hill, in the parish of Tough (O.S. 6 inches, Aberdeenshire, sheet Ixiii.), is a similar monolith, also called Lulach’s or Luath’s Stone; and the tradition attached to each pillar is that it marks the place where Lulach, stepson of Macbeth, was overtaken and killed after his father’s defeat and death at Lumphanan (15th August 1057). The historical facts about Lulach the Fatuous are briefly as follows. He was a son of Macbeth’s wife, Gruoch, by her previous husband, Gillacomgain, of the ancient house of Moravia, and himself a cousin of Macbeth. After Macbeth was defeated and killed by Malcolm Canmore, Lulach carried on his stepfather’s claims, but himself was killed at Essie, in Strathbogie, on 17th March 1058, and, like his stepfather, was buried in lona. Two sources aver that Lulach was killed by Malcolm in battle, but another says that he died by treachery.
From the April 12 1926 Proceedings of the Scottish Archaeological Society. Online here via the ADS:
ads.ahds.ac.uk/catalogue/adsdata/PSAS_2002/pdf/vol_060/60_273_280.pdf