Do you know who William and Lillas' children are (other than Alexander) and if any of them married a Fraser?
My hypothesis is that Alexander's sister married a Fraser and this couple had children. One of those children would be my Great-Great grandfather, Thomas Fraser. According to J.P. MacPhie in "Pictonians at home and abroad : sketches of professional men and women of Pictou County, its history and institutions," Thomas Fraser, a state Senator from California (and my g-g-grandfather) and Alexander Blaikie were descended from Alexander Cameron, who came to Pictou on the Hector. I also have a letter from Alexander Blaikie to Thomas Fraser in which Alexander Blaikie notes that he is Thomas Fraser's uncle. Thus, you see where I got my hypothesis.