Monica
The parents given on the marriage certificate for William Murray (21), coalminer, who married Agnes Brown (16) in district of Calderhead, Lanark, in 1877 are Peter Murray, tinsmith, and Mary Flood. Marriage after banns according to the forms of the Roman Catholic Church. So same parents as death certificate I'd say.
William born to Mary Flood and Peter Murray 23 December 1854 baptised 9th January 1855 in Catholic Registers on SP. I haven't downloaded the image to see what detail is there.
Dod