The IGI has an extracted entry (from the parish reg.) for Thomas Fletcher Dougherty, Birth: 06 JUN 1878 Laxey Hill, Lonan, Isle Of Man. Father: Fletcher Dougherty, Mother: Catherine Cowley, for their 2-year-old son b.Lonan in the 1881 Lancs census.
There are several children's births registered to this couple in Brian Lawson's index, including Percy aged 7 months in the census [born] 1 Sep 1880 [ref.] Dou 285.
For the others see: www.iomfhs.im/lawsons/births/da.html
There are children's births up until 1893, so I assume they returned to the IOM (or Catherine did for the births). If you buy some of the certs using the refs given they will give addresses, occupation, etc.
Did you see there are two census entries for father Fletcher in the 1881 census? One at home, and the other on the Vessel "Tynwald".
Catherine [Cowley] also aged 25, b.Lonan.
Possible bapt: 29 NOV 1857 Lonan, Isle Of Man, Father: THOMAS COWLEY, Mother: JANE GORREY [IGI].
Lancashire Marriage indexes for the year: 1877
Surname Forename(s) Surname Forename(s) Church / Register Office Registers At Reference
DOUGHERTY Fletcher COWLEY Catherine Wavertree, St. Bridget Liverpool 2050WD/1/35
Sue