Glad to be able to still help- the reason for nil father being recorded is that those children would have been born out of wedlock.Some time the mother in these cases may include the fathers name and/or surname into one of the names of the children- so have a look there for a clue!!
It seems you question re Lily has already been answered re Ida Clarice NEWTON and Melvia Jean Lambert NEWTON
I checked SA marriages to 1937 and deaths to 1972 as far as my records go and could not find anything further in SA- perhaps they moved to another State.
I hope this may help Good luck Kind Regards Gordon