How did they determine it was OK to run the Bluebird and operate the aircraft on the Lake?
Clinton, they take core samples with a small hand-operated auger to determine the salt crust thickness. The salt crust is 1M thick at Lake Eyre, at Level Post Bay.
Australian salt lakes are nearly all very treacherous, with a thin crust of salt, and sticky, fine clay mud underneath. That mud can vary in depth from a few hundred millimetres to dozens of metres.
There are very few Outback salt lakes that can safely carry the weight of a vehicle or aircraft.
Claypans, which often appear very similar to salt lakes (although they're usually darker in colour), are nearly always safe for vehicles and aircraft, if they're dry.