Hi there!
I am grateful to find this thread.
Lucy Gilmore Wright (Susannah Wright’s daughter) is my great-great grandma (married William John Mitchell in Croyden, came to Canada in 1911 or so, passed away in Canada). 
I have had very little success searching her on Ancestry so this has been amazing to stumble upon. 
I am curious about the “gilmore” middle name and about who her parents are.
Hello and welcome to Rootschat  
 
Do you have her 1967 death certificate?
1967 Lucy’s death gives parents as Abel WRIGHT & Susan GILMORE, 
spouse William John MITCHELL 
https://www.familysearch.org/ark:/61903/1:1:FLY9-DMT (no image)
1911 census Lucy MITCHELL her husband William and children are living in Croydon
https://www.familysearch.org/ark:/61903/1:1:XW8V-9M7
Not sure if these were posted possible entry for Lucy's birth entry from GRO indexes and that of her sister Kate Gilmore Wright both mother's name have been left blank which would indicate illegitimate, Kate's baptism details on the thread show NO father named only mother Susannah WRIGHT
Just speculation perhaps Gilmore might be the surname of the father  
 
WRIGHT, LUCY   -
GRO Reference: 1884  M Quarter in KINGSTON ON THAMES  Volume 02A  Page 357   
WRIGHT, KATE  GILMORE   -
GRO Reference: 1882  S Quarter in KINGSTON ON THAMES  Volume 02A  Page 352   
I don't know whether SarahEliza has either birth certificate of the girls to confirm the details or if she obtained the marriage entry posted by Rosie99 to check if she's the correct Susannah
Jun 1901   
Walters    Henry        
Wright    Susannah        
Croydon    2a   621 
Hopefully when she receive these notifications she will be in touch and may be able to help you further.
EDIT to add these appear to be sons William & Roland's birth entry - also no mother's maiden name
WRIGHT, WILLIAM       -  
GRO Reference: 1880  S Quarter in KINGSTON ON THAMES  Volume 02A  Page 308
WRIGHT, ROWLAND       -  
GRO Reference: 1885  J Quarter in KINGSTON ON THAMES  Volume 02A  Page 330
Here's the link to GRO https://www.gro.gov.uk/gro/content/certificates/login.asp it's free to search 
but you have to register to do so
Interestingly Lucy's brother lists Abel Gilmore Wright (valet, deceased) on his marriage certificate!
https://www.ancestry.ca/sharing/26349295?h=e4ae71&utm_campaign=bandido-webparts&utm_source=post-share-modal&utm_medium=copy-urlLondon Metropolitan Archives; London, England; London Church of England Parish Registers; Reference Number: DRO/150/010