Try looking up the Birth Record of Lizzie Dorans in Kilmarnock on ScotlandsPeople. Birth Records usually show marriage records in Scotland if they exist. It turns out that Lizzie was born illegitimate and there was no marriage although the father David DORRANS added his name as father to the record. Mother's name is listed as JANE Duffy and father's address is given as 7 Fleming Street, Riccarton. Lizzie's name is recorded as LIZZIE DUFFY DORRANS. Then you can try accessing her DEATH RECORD. There is one listed for a Lizzie DUFFY (b 1907) in Kilmarnock for 1982. You may be able to find the Death Record for David Dorrans too. There are 3 listed for the County of Ayr after 1925.