Nothing I found exactly matches your information.
How sure are you about Thomas place and date of birth?
Here is what i did find in the census.

The IGI gives three likely christeninings of a Thomas Killip post 6 April 1854
1. Thomas Killop May 7 1854 in Whitehaven, the son of Thomas Killop and and Ann.
He appears in the 1861 census in Whitehaven RG9/3946 folio 78 page 49 aged 7, with Ann Killip 42 b Egremont, John Callow (stepson?) 19 b Whitehaven, Ann Callow (stepchild?) 16 B Whitehaven.
There is a Thomas Callow 32 Mate on a ship b KK Lonan Isle of Man.
Ann was a widow in the 1851 census.
In 1871 (RG10/5253 folio 25 page 44), Thomas is living with John Callow at 50 New Town in Whitehaven:
John Callow mar head 28 Seaman in merchant service b Whitehaven
Elizabeth wife 28 b Whitehaven Elizabeth dau 2 b Whitehaven
Thomas Killop brother-in-law b Whitehaven.
In 1881.

In 1881 Brick Field, Millom Cumberland RG11/5197 folio 40 page 73.
Thomas Killip head Mar 26 plumber b Whitehaven
Elizabeth wife 23 b Egremont
Ann E Killip 9 months b Millom
I did not find the family in the 1891 or the 1901 census.
A Thomas Killip married an Eliza Wilson in the June quarter of 1878 in Bootle volume 10b page 914.
A Thomas Killip married Ann callow in Whitehaven in the December quarter of 1852 vol 10b page 616

2. Thomas Edward Killip July 12 1854 in Castletown, Isle of Man, the son of James and Catherine. Ther is no marriage in the IGI for this couple and I could not locate him in the census records.

3. Thomas Killip: January 7 1855 in Lonan Isle of Man, the son of John Killip and Isabella Faragher. He appears in the 1861, 1871, 1881 and 1891 census.

There is another family in the 1861 census in Liverpool with an 8-year-old Liverpool-born Thomas Killip and both parents, Sarah and James, were born in the Isle of Man. However he appears to have been born in Liverpool the June quarter of 1853 vol 8b page 146.