Try to find the spot where the photographer was standing.
The Dominican Church, Baker Place.
The Dominicans moved from Fish Lane to Baker Place in 1815.
The Church was designed by the Paine Brothers "Gothick Style"
Why was this place called Baker Square?
According to Limerick City Placenames (a .pdf document), it's called Baker after Richard Baker, who built the houses on Baker Place.
James Dowd's book "Limerick and its Sieges" credits a cropped version of this image to William Lawrence. Given that the book was published in 1890, this image would seem to date from c.1880 to c.1890. See also discussion on higher res image (possibly earlier still):
Geohive 25" OSI map link.
Just replaced this photograph with a higher res version...