Hi Selina,
I was just having a quick look at your Great-Grandfather Thomas Lawson Carruthers and where you have mentioned that he has a connection with New Zealand. Looking through New Zealand's BDM I have found the match that you have mentioned where he has married Sarah Maria (nee. Cotterill) on 7th July 1905.
They had a daughter, Stella Constance Ethel Carruthers who was born on 25th March 1906 and you will be happy to know that she wasn't one of his illegitimate children, being born in wedlock. Unfortunately, by August 1913 as per the below article, a decree nisi had been approved by the court at the Palmerston North sittings for the pending dissolution of marriage.
(Manawatu Standard, NZ, Wednesday 20 August, 1913)
Unfortunately I had no luck in finding any shipping information of when Thomas might have either arrived or left New Zealand.
Trev