Hi jayandjay
What is the name of the child you know about? Is it one of the following?
https://www.familysearch.org/https://familysearch.org/search/collection/igiAll baptised (in years shown) at TULLYNESSLE AND FORBES AND KEARN,ABERDEEN, issue of John LAWSON and Katherine ANDERSON:
Anne 1816
William 1818
John 1821
Beatrice 1823
Eliza 1826
James 1831
Alexis 1834
Which appears to be this family:
1861: 3 Farquhar Pl., St Nicholas Aberdeen, Aberdeenshire
Head: John LAWSON 73, retired miller, b Alford Aberdeen
Wife: Catherine 72, b Kerriemuir, Forfarshire
Son: John 39, Photographer, b Tallynessle, Aberdeenshire
Son: James 30, Clothier, b Tallynessle, Aberdeenshire
Dau: Alexis 27, Whiteterer's?

?woman, b Tallynessle, Aberdeenshire
Visitor: Elizabeth MAIDEN 18, Domestic Servant, b Rhynie, Aberdeenshire
If your John died 1868 in Scotland, and if the informant knew the details, his parents names should be on his death cert. And if the above census John is your John, then Catherine lived past 1855 and therefore same thing for her - parents names should be on the death cert.
You can search for and purchase Scottish records here:
http://www.scotlandspeople.gov.uk/welcome.aspxOnce we know if this couple on the 1861 is your couple or not (by identifying the child of your couple that you know of) , we can hopefully dig you out a little more info.
Cheers
AMBLY