Is he the one born Apr,May,Jun qr 1902 registered Croydon, UK?
His full name, then, is Charles William P LUNNON. As I said before there is a Charles William LUNNON on the electoral rolls, and now we have his full name this person seems more possible:
1931
District of Gippsland, Subdivision of Lindenow,
Charles William LUNNON, Stockdale, stockman
There seems to be only this one entry for this name, but I do not have access to Sth Australia rolls, or to NSW until later - he may well have moved on.
No likely entries for marriage or death on NSW BMDs but births are only up to 1909 so can't find any children in NSW for him.
Cheers, Judith