In 1901 John and Annie have a nephew Walter Lawson bc.1877 Partick with them.
Traced back this Walter and he was born 6/11/1876 Partick, illeg. son of Walter Lawson, carter, and Agnes Fergusson. Don't think they ever married (was hoping to see who his father named as his parents) BUT Walter Lawson senior died in 1893 - his death certificate shows his parents as Peter Lawson, carter and Margaret, nee Hay.
The 'Robert' shown as John's father on his marriage certificate is incorrect and should read Peter.
Both John Lawson and his brother Walter Lawson were creative with their ages on the census - John Lawson born 18th May 1839, bp.30/6/1839 Dollar, Clackmannanshire and Walter Lawson b.28/7/1849, bp.26/8/1849 Dollar, parents Peter Lawson and Margaret Hay. In 1841 Peter and Margaret are in Dollar, with John aged 2.
Found John's death certificate - he died 30/11/1912 Maryhill, Glasgow as John Hay Lawson, certificate confirms his wife as Ann Watt and more importantly for you, his father is named as Peter Lawson, carter (dec'd) and mother as Margaret nee Hay (dec'd).
In 1851 Peter, Margaret and their children are in Tillicoultry - includes both John and Walter.
Annette