The temperature in the ISA reduces with altitude at a rate of 1.98C per 1000ft.
The air is not moving up or down; it is stationary. If an observer travels up within the atmosphere, he/she will experience colder temperatures as the altitude increases.
If a parcel of air is lifted through the atmosphere, the parcel will expand and cool. The rate of cooling depends on the humidity of the parcel. These rates of cooling are known as lapse rates and have nothing to do with the ISA model of temperature reduction of the atmosphere itself.
The resulting temperature of the parcel at its new higher altitude may differ from the temperature of the surrounding atmosphere. If the parcel is warmer than its surroundings, it will continue to rise. If the parcel is colder, it will want to descend.
I think Suade is confusing the two concepts:
1. The reduction in temperature with altitude of the stationary atmosphere; and
2. The cooling of a parcel of air as it is lifted within the atmosphere.