It looks like the issue is much more complex.
Although the first wife of Alexander Fraser of Lovat is named Elizabeth Keith, there seems to be no sources that name her family or connections. His second wife, was Marion Keith, the daughter of Sir Robert Keith and sister of William Keith. See The Scots Peerage, Vol. 5, p. 521. It would be fairly unusual for there to be no mention of the fact that Elizabeth and Marion were sisters it that was the case.
The Scots Peerage in that volume does state that Alexander's daughter, Marjorie did marry William Keith, and also in Volume 6, page 40 that there was a commission to grant dispensation of the marriage issued on 26 April 1414.
However The Complete Peerage, 2nd ed., Vol. 8, states that if the marriage did take place, then there was another wife named Mary or Mariota before 1436 who was the mother of his eldest son Sir Robert Keith and probably of the rest of his children. Mary died on or before 1442.
This parents of Mary are unknown, although The Scots Peerage (Vol 6 again) does say that she is "usually said to have been the daughter of Sir James Hamilton of Cadzow but there is no evidence for this and the dates make it doubtful"
It's unfortunate that the only source already on most of these profiles is from thePeerage.com, and the only source used on that website is Burke's Peerage and that isn't a good source for the medieval period.