Hi Jenie
I too had family living in Lumsden Street including two infants who died within 24 hours of each other from Whooping Cough, although this was 1878 so probably just a bit too early. I have the marriage record of their parents but it just says "The Parish Church" which I believe was St Pauls.
As for where Lumsden Street was, this description may help:
"Interspersed within the triangle formed by Mandale Road, George Street and Darlington Street (now part of Thornaby Road) were a collection of residential streets perhaps forgotten now, like Caledonia Street, Carlisle Street, Lumsden Street, Cross Street, Hibernia Street and Butterwick Place."
My Dad was born in Darlington Street and remembers the old area well - he's not so great on the churches but still drinks at the club in Thornaby every weekend without fail!
I seem to remember seeing a map on a chat site I'm on- could take a while to find but if I do I'll let you know.
PS - Another thought. To narrow down the potential infant birth / deaths have you tried the Stockton Roots website. Their records cover Thornaby 1875 - 1948 but exclude the wider Middlesbrough area. If you start with the deaths then cross reference those names with births, then exclude any years you already have surviving children for, you should hopefully have a manageable number to look into further.