Think winter months for the "season" and you won't be too far wrong. Summer flying anywhere in Central Oz is a bummer with thermal turbulence etc.
I enjoyed flying there back in '09 although there is a sameness to the flights, especially when you are doing your third for the day and you have to run the whole spiel yet again. The flies never let up (you are in the middle of the largest working cattle station in the world) and you certainly learn all about cross-wind landings and dust storms.
The run up the Warburton River was always fascinating, probably more than the lake itself, especially if you were lucky enough to bag a charter through to Birdsville where you could follow the river to the Goyder Lagoon then up the Diamantina to Birdsville. Great country.