Lutheran schools are accredited by the relevant state government authorities in Australia under the various education laws in place.
This does not indicate that they are independent of the education laws of Australia, only that their governing bodies are managed privately.
The Australian Bureau of Statistics reports that there are 83 Lutheran schools which make up 6.4% of that total, being the sixth highest group when viewed by percentage of students attending.
This is in contrast to some other Christian educational institutions, which take into account other non-religious criteria.
To useful books on the subject: The Patriarchs: A History of Australian Lutheran Schooling 1839-1919 by Richard J. Hauser The Pathfinders: A History of Australian Lutheran Schooling 1919-1999 by Richard J. Hauser Both available from Amazon in Kindle format.