Unless the Aussie doc proponents can show a Lavender as a Registrar too who worked in ...South Australia. What are the odds?
Sure - Eric Lavender. He was the Deputy Registrar General, Customer Services, for South Australia by 1990, which to me suggests he was quite possibly in a more junior position in the 1950s and 1960s.
If the Kenyan Lavender holds up, the Aussie doc is a fake.
The odds are 0%, because Miller and 44B 5733 are also in common.