As the air rises (and expands, thereby decreasing in air pressure) it cools, resulting in the adiabatic lapse rate that you mentioned.
(the air; rises; ) (the adiabatic lapse rate; mentioned; you) (the air; expands; ) (the air; decreasing; in air pressure) (it; cools; T:As the air rises (and expands)
the air the adiabatic lapse rate the air the air it
rises mentioned expands decreasing cools
you
in air pressure
T:As the air rises (and expands