I would like to bring to your attention a thermodynamic property which I havn't given very much attention until recently. It is the thermal diffusivity, that is the rate at which a temperature change will spread in the medium. Quoting from the G&T paper:
In particular you should pay notice to the density term occuring in the expression for the thermal diffusivity. In many cases the density appears to be a trecherous quantity. The reduction in density with height explains why the equilibrium state may very well be isothermal. Ironically however, if we adopt the non-equilibrium approach this non-uniformity might very well explain why the lapse rate is steeper closer to the surface than higher up. Maybe it could even explain why the stratosphere is stratisfied: Since the density is so low the thermal diffusivity is so high that any temperature gradient will quickly disappear. At least it is worth to think about.