Look up at Lancashire Archives

[BumbleB]

Transcription of 1901 Ireland Census entry for Edward.

https://www.findmypast.co.uk/transcript?id=IRE%2FC1901%2F9825899

[heathers]

the death looks as if it will fit into the equation as well - I'd been wondering about her as well.
The fun thing about doing a One Name Study is you learn a lot about different families,  so its the odd ones that are an exciting challenge.

Sue

[Ladyhawk]

Possible:

Ancestry have a birth registration for Elizabeth Astley Horsman - 09/1902 - Belfast.  FindMyPast have the same entry.

Plus 1911 Ireland Census - daughter of Edward and Annie Sophia Horsman - address shown as Harbour Street, Pottinger (part of) Down, Ireland.  Birth given as about 1903.

Added:

Transcription of 1911 from FamilySearch   https://www.familysearch.org/ark:/61903/1:1:QYFL-TK2M

Elizabeth’s  baptism 17th June 1902  mn Ellison
https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1902/01903/1738797.pdf

1902 Marriage of Edward Horsman & Annie Ellison
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1902/10260/5734201.pdf

[Ladyhawk]

I wonder if this is relevant to the mother BumbleB found

Deaths Dec qtr 1958   
HORSMAN    Annie S M   
age 84   
Darwen RD    10c   108

Annie Sophia Mcgowan Horsman
Register Type:   Cremation
Death Date:   11 Dec 1958
Burial or Cremation Date:   15 Dec 1958

Annie Sophia Horsman widow of 19 Blackburn Road, Rishton
Death 11 Dec 1958
Probate 20 May 1959 to Arthur  Horsman, cotton mill overlooker
Probate Registry:   Lancaster

[heathers]

I think she must have been living with daughter Elizabeth Astley H when she died.
I'll get the new info on my system,  and it will become much clearer. 
I reckon the Arthur of probate would be her SIL - the occupation is right.

Sue

[heathers]

Just looked at the marriage record, wher Edward described his Dad as a 'Lead Merchant' .  Census records show he was a plumber !

Sue

[Maiden Stone]

Perhaps a plumbers' merchant, selling lead piping among other items.