I believe that James Battista 'reinvented' himself with the surname Mathews/Matthews.
We know from RTL's look up that he was born 18th August 1899.
St Cuthbert RC baptism
Jacobus Battista
Born 18 August 1899
Bapt 6 Sept 1899
Son of Joannis & Elizabethae (Helene?) olim Lawson
Grandparents Donatus Alvini & Jane Reid
Using the free search on the 1939 register I looked for the surname Matthews (with variants) in Newcastle upon Tyne with that birthdate. I didn't find anyone, but extending it to one year either side I found a Thomas G Matthews born 18th August 1898.
In the same household was a Lily Mathews born 1915 and a James V Matthews born 1939.
freeBMD shows a Lily Macauley born Newcastle upon Tyne 3rd q. 1915 and a quick check on the 1939 free index confirms Lily Mathews' month of birth as August.
free BMD shows James V Mathews born Newcastle upon Tyne, 3rd q. 1939 mother's maiden surname Macauley
There are three other Mathews births in Newcastle upon Tyne between 1933 and 1938 mother's maiden surname Macauley. Two of them have the middle initial 'B'.
We know that he married as George J. Battista alias George J. Matthews and it seems to me that by 1939 he's become Thomas G Matthews.
I am still hacking away at the very edges of this family, and think I might have discovered what happened to Lily Macauley/Battista/Matthews. I am being very careful with names as some of the people involved may still be alive.
Lily and James appear to have had four children all of whom were registered with the surname Mathews (i.e. one 't')
It looks like the son who was with them in 1939 died in Coventry in 2006. The date of birth on his death registration is identical to that on the 1939. This son also appears to have married in Coventry in 1961.
I noticed that another of their children married in Coventry in 1952.
Then I noticed the birth of two children in 1946 and 1948 in Coventry whose births were registered as Mathews cross-referenced to the surnames Matthews and Smith. In both cases the mother's maiden surname was Macauley. There was also a possible child born 1945.
There was a marriage in Coventry in 1949 of a Lily Macauley and a Charles Smith, followed by the birth of a child also in 1949.
There was then the death of a Lily Smith aged 51 (i.e. born 1915/16 - we know 'our' Lily was born in 1915) in Coventry in 1967. An article in the Coventry Evening Telegraph indicates that this Lily had a husband named Charles and a daughter whose christian name matched that of the child born in 1949.
My feeling is that this is very likely 'our' Lily.
I have sent full details including names to Sophie by PM.