For the record the death certificate can be viewed via a tree on Ancestry.
27th May 1900, St Joseph's House, Newcastle upon Tyne
Hannah McLane aged 76, widow of John McLane, General Labourer.
Of 126 Fairless Street
Informant John McLane, son, in attendance, of 97 Fairless Street (he is still there in the 1901 Census)
Where Avondale Road, as mentioned in the newspaper announcement, come into is unclear.
I think the tree with the death cert may imply that Patrick McLean was her son.
Patrick McLane is on the electoral registers at 126 Fairless Street from 1894 to 1900
Probably then he is the Patrick McLean at 42 Beresford Street in 1901, age 52, Labourer, born Ireland, married to Mary, born Gateshead, with children and it looks like with step children.
Beresford street was in the same census enumeration district as Avondale Road.
https://www.familysearch.org/ark:/61903/1:1:XSMT-GP71902/3 electoral has Patrick
McClen at 42 Beresford Street.
Unfortunately there may be a missing year in the Newcastle electorals on ancestry, 1901/2, which might have confirmed a move from Avondale Road.
But in 1903 we have Patrick McClen at 85 Avondale Road, successive from 42 Beresford Street!!
Later in the decade Patrick McClen is at 91 Avondale Road. And at more numbers too.
Patrick McLean age 60 is in the 1911 census free index, wife is Mary, I would imagine in Avondale Road
https://www.familysearch.org/ark:/61903/1:1:XWM8-Z2FI think Patrick and Mary married in 1900 in Newcastle.
Patrick's death?
June 1927 Newcastle T. 10b 179
Mclean, Patrick
age 77
He is in the Jesmond indexes found through the link from Jen in
Reply #20, and we do at least have a grave register entry for him
Unconsecrated section D, grave 393 (there seem to be several D sections)
Patrick was first in, a bit disappointing. Buried 2 June 1927.
https://www.familysearch.org/ark:/61903/3:1:3QHV-L3VC-GWB5