What & where was 'Bower House Fold' Blackburn, 1861

[Kay99]

From Kay's list:
'Bower House Fold Lane (1848) Livesey now Shorrock Lane'

Added:
Bower House Fold (1786-1959) Primrose Terrace Livesey

Primrose Terrace next to Bower Street  https://maps.nls.uk/geo/explore/side-by-side/#zoom=17&lat=53.7368&lon=-2.5075&layers=6&right=BingHyb

[Maiden Stone]

Bar House may have been the tollbar-keeper's house.

[Maiden Stone]

Was this building connected to a Cotton Mill? If yes, what would that Cotton Mill be called?

Lists of mills in Blackburn:
https://en.wikipedia.org/wiki/List_of_mills_in_Lancashire#Blackburn
Introduction to list of mills in Lancs. says it is incomplete. Also, I noticed that some mils which were in Rochdale are listed under Ramsbottom but there is no heading for Rochdale, so there may be other errors.
Grace's Guide to British Industrial History
https://www.gracesguide.co.uk/1891_Cotton_Mills_in_Blackburn
This lists only those operating in 1891. (Info from Worral's Cotton Spinners' Directory)
You can see from the lists that there were a lot of mills in Blackburn. 
I spotted 3 nearby on the map in Stan's post. Plenty more within walking distance. You can look at maps from different years on that site.
The family may or may not have lived in a building owned by an employer.
The Lancashire Cotton Famine, a consequence of American Civil War was in 1860s. Mills closed. When they began to reopen, people probably worked for whoever was hiring.

[jan21]

I looked at an old map but if you look at todays map, and if you look up bower st now, opposite is a primrose Close. On this land was Bower House Fold, it has a railway line behind it.  There was a lot of mills and factories around this area and would have been very built up with workers houses. A plot shows on the 1924 map that it had an area directly adjoining the railway track that had been left vacant, showing some platform or underground railway connections, this is now built on and is where Primrose Close has houses on it. My friend lives there. xx