The Lewis Killip who was a police officer in Liverpool from late 1870s to late 1890s and later a security worker in Liverpool docks and who died in Liverpool in 1923 appears to be the same person as the Lewis Killip born in Lonan in 1855 - there seem to be no other records in England prior to 1881 and are no other Lewis Killips in the Manx records after 1871 that fit even loosely (he is shown in 1871 aged 15 at Ballacojun, Lonan with his older brother Thomas 27, his widowed mother Ann 60 and sisters Ann 26 and Catherine 23 and a couple of nephews. His father James died in 1866. Assuming him to be the same person, his ancestors were in the Ballaugh area when records began and seem to have moved to Lonan parish in the early 1700s.
On the Lonan-Douglas issue, Brian may be correct in that enumerators may have regarded Douglas as a synonym for the Isle of Man - in later Civil Registration Lonan is a sub-district of the Douglas area - so this may be a factor. As he was a lodger in Liverpool in 1881, 1891 and 1901, it would have been the Head of household who presented the information to the enumerator (in 1881 he is shown as from Lonan, in 1891 as Louis from Isle of Man and from Douglas in 1901 when he is also shown as a widower lodging with Catherine Cain, a 69 year old widow - possibly Catherine was not precise in her knowledge of Lewis's background- I have not come across any record of a marriage for this Lewis Killip)