It's all to do with changes in the lapse rate, regardless of what's causing the warming. (skepticalscience.com)
The warming effect near the tropopause level from CO2 can be explained by the relatively sharp change in the lapse rate. (realclimate.org)
Most of the moisture is found below about 10,000 feet, so that is where the effect of changes in lapse rate will be felt, and the effect of an increase in moisture is to decrease the near - surface lapse rate, potentially resulting in an important negative feedback on radiative forcing. (judithcurry.com)