Don't know if anyone can help for a birth record for a THOMAS JOHNSTON, born 1845 in Armathwaite
Are you sure it's
Armathwaite? It's not uncommon to find
Arrowthwaite - part of Whitehaven/Preston Quarter - transcribed as Armathwaite.
There's a Thomas JOHNSTON 3 Whitehaven in the 1851 census - but his mother was Mary

Thomas JOHNSTON 7 Whitehaven in Cockermouth - mother Sarah.
Thomas JOHNSTON 7 Whitehaven in Muncaster - with BOWS grandparents - daughter Ann was apparently bap 1814 Muncaster (IGI).
There is a possible marriage which may be worth following up ...
Marriages Dec 1842
Bell Joseph Whitehaven 25 188
BOWES Ann Whitehaven 25 188
CASSON John Whitehaven 25 188
Johnston James Whitehaven 25 188
LANCASTER Sarah Whitehaven 25 188
Scott Mary Whitehaven 25 188
Muncaster is very close to Ravenglass.
Ann JOHNSTON (mar) 35 Ravenglass was visiting someone in Hensingham (1851)
You may have trouble with the birth of Thomas
Births Jun 1843
JOHNSTON Thomas Whitehaven 25 1[60]2
JOHNSTONE Thomas Whitehaven 25 152
Births Jun 1844
JOHNSTON Thomas Whitehaven 25 133
Births Sep 1844
Johnston Thomas Whitehaven 25 154
Births Dec 1844
JOHNSTON Thomas Whitehaven 25 146
1861
ArrowthwaitAnn JONSTONE (mar) 45 Householder, Ravenglass (no husband in sight)