I should add that Crowley and Crawley are often confused in the records. (the 1901 census and Brian's marriage index both show Crawley).
I did not find James anywhere, but there was a possible relative:
There is a West Derby marriage of Timothy Lambert Crowley to Margaret Duggan in the July quarter of 1868 and birth to a Timothy Lambert Crowley in 1869. They are in the 1871 census in West Derby.
Timothy Crawley head Commercial Traveller 43 b Ireland
Margaret wife 34 b Liverpool
Timoth L son 21 m b Liverpool
Florence Jno son! 6m b Liverpool.
He does not appear again but Florence does in 1881 as an adopted daughter of Jane Howley Widow.

Also Brian has burials for other Crowleys:
John Parfitt 1y6m Douglas 10 July 1901
Doris Ceclia 17 Douglas 7 Feb 1923
Eveleen Mary 2y5m Douglas 30 Mar 1907
Henry Lambert 2 Douglas 2 Aug 1904
Lydia Maud 13m Braddan 20 Apr 1887
Madge Annie 19 Douglas 111 dec 915
Nora Catherine 27 Douglas 11 Feb 1937