That's a bit beyond my area of expertise. No doubt the lake environment will present challenges to mining but we have good mining engineers and hydrologists in WA so I don't think these lakes will represent insurmountable problems if there is a big enough deposit to justify mining. I've spent a lot of time on these sort of lakes and they are often navigable with light vehicles under dry conditions. Because they are generally the lowest landforms in an already largely flat landscape they are the natural collectors of water after heavy rains so can get problematic in the wet.
I'd say in a mining situation you would need to prevent the run off from the natural catchment areas from impacting the mining zone by using dams and pumps to divert the natural water flows.
Sunrise Dam is a large gold mine on the edge of Lake Carey, 50km south of Laverton in WA, which is impacted by a salt lake environment (amongst other mines that I could name in WA) . The mine falls in a zone of salt pan lakes and gypsum rich sand dunes on the eastern edge of that lake which is a much much larger lake than lake Austin (see the GoogleEarth image below). I'm not sure how heavily impacted Sunrise Dam was by its location on the edge of the lake (probably would have been worse if it was more centrally located in the lake) but it didn't stop the mine being developed both as an open pit and an UG development. The open pit is reported to have reached a depth of 440m in 2008 and in 2007 it produced 600,000oz of gold (including 80,000oz from UG).
As said if there is enough gold people will find a way. Esh