Hi Mike,
The 'lapse rate' is the observed temperature drop with increasing altitude that results from the vertical pressure gradient matching the earth's gravitational pull and treating the atmosphere as an ideal gas. By the ideal gas equation, the air temperature is proportional to the pressure so that a drop in pressure will cause a proportional drop in the temperature, ie. pv=nRT where p:pressure, v:volume, n:number of moles, R:Avogadro's constant, T:temperature (this is from memory, correct me if I'm wrong).
Cheers,
Paul