You can find Sowerby Street by searching Historical Directories www.historicaldirectories.org
Post Office Directory of Cumberland and Westmoreland 1873
Carlisle
Botchergate, from Court Square
Nos 1 to 43
........ here is Portland Place
Nos 45 to 51
........ here is East Street
Nos 55 to 63
........here is Irving's Place
Nos 65 to 69
........here is Sowerby Street
Nos 71 to 91
........here is Tait Street
Nos 93 to 105
........here is William Street
Hope some of these still exist as reference points
regards