Going by Death Record, YOB for Walter Laurens and your thinking his Parents may be Jean/Jane;
1871 Census
Handois?,
St Lawrence, Jersey, Channel Islands
RG9/4402/44/1
Jean LAURENS, 48, Head, Mar, Farmer, born St Lawrence
Jane, 46, Wife, Mar, born St John
Philip, 15, Son, Scholar, born St Lawrence
WALTER, 13, Son, Scholar, born St Lawrence
Lambert, 10, Son, Scholar, born St Lawrence
Lavinia, 8, Daug, Scholar, born St Lawrence
Adolphus, 4, Son, born St Lawrence