CP,
There is no SBAS coverage in Australia for aviation.
There are no approaches designed/promulgated to LPV minima in Australia.
At least in the avionics I am familiar with (my caveat) you need to select/check the augmentation provider (WAAS in the US for eg) when you load an LPV. I would expect if the augmentation service is not available/being received, then you would/should get alerting that the LPV approach you are attempting is not valid. Regardless of the avionics, the approach chart in OZ wont have LPV minima, so you cant fly in LPV mode anyway.
In OZ you have RNAV NPA (LNAV minima) or RNAV APV (LNAV/VNAV minima). Both use the barometric altimeter for height awareness, APV has the (usually) 3 deg GP designed into the approach and coded in the system, the NPA does not. The NPA uses intermediate step heights instead of a GP.
You can search for 'LAX RNAV Approach' to look at an RNAV(GPS) chart (not the RNP chart - Flight Aware website is good) to see the 3 different minima boxes - LPV, LNAV/VNAV, LNAV.