jesslorla on Family Tree Circles

Would love to be able to find a birth certificate for my great-grandmother, Mary Lilian Gannon, born 23 November 1891 in Melbourne, Australia.
Father: John William Gannon.
Mother: supposed to be Jessica Lawler / Lorla / ??, she died in childbirth having Mary Lilian.
In 1892 John was living in Melbourne with his sister Mary Francis Gannon (by then Mary Francis Thompson), and her husband, James Thompson.
Mary and James Thompson, having recently lost a little boy in childbirth, effectively adopted Mary Lilian.
There are two birth certificates that could be Mary Lilian:

1. Lillian May Gannon, mother Mary Francis Herbet and father Jas Gannon.
Note: Mary & James Thompson’s eldest son was named “Francis Herbet”, so perhaps this is the right link?
2. Mary Agnes Gannon, mother Gannon, father JNO Gannon, Dated 1891, ref # 19602.
Death certificate for Jessica Lawler / Lorla … nothing located.
Links between John William Gannon and the mother of Mary Lilian, nothing found.
There are newspaper references to John William Tailor shop / working at in Sydney, and later bankruptcy in Hobart.
Eventually, John William, Mary Lillian and Francis & James Thompson returned to NZ, settled in Mangaweka where Mary Lillian grew up and later married John Collis. They had 2 children, Selwyn and Desma. Desma was my Grandmother and she talked of very happy times growing up in Mangaweka.
Very keen to know who Mary Lilian’s mother was and what happened to her, any help very much appreciated.
This links to post on this site 16 June 2018.