I have what may be the driest patch of lawn in the uk. On a 30 degree slope, on chalk, on top of a large soakaway crate, in the South East of England on the south face of a valley with a localised dry microclimate. The rest of the lawn just about survives but in the 2x2 m patch over the soakaway the grass regularly dies. I've tried heavy mulching (coir) but it soon disappears and I would much rather garden with my soil conditions, rather than fight them: elsewhere I have a wonderful small chalk meadow.
So it's 2 feet of chalky soil, over a few feet of compacted chalk over a soakaway crate set in chalk bedrock.
I am inclined to give up on this patch and maybe put a plinth or statue there. It has been suggested that I should try growing a large cactus- any suggestion as to what may thrive there. There's plenty of sun but it it's also exposed to wind.