To make air parcels move up or down, we need the air temperature inside the
air parcel to be different from the temperature of the surrounding air. Heating
the air at the ground makes positively buoyant, warm air (this would be considered
a diabatic process, since heat is added). This would be a common technique on
sunny afternoons.
Another way is force air parcels to move or or down. This could merely be natural atmospheric turbulence, which contains an occasional up or downward motion to nudge air parcels around. Forcing the air parcels to move will cause them to expand or compress adiabatically.
Since atmospheric pressure decreases with increasing altitude, a parcel adiabatically expands when it rises, and therefore loses temperature. In Earth's troposphere, an unsaturated parcel of air loses temperature at a rate off 10°C/km.
In the ambient environment, the lapse rate can be anything, owing to variations of heating of the atmosphere by the ground and by the sun and weather conditions, such as wind and clouds. This environmental lapse rate does not affect the lapse rate within rising/sinking air parcels.
The end result of making an air parcel rise/sink adiabatically is that the
parcel temperature and the environmental temperature can change at different
rates, which means that the parcel and the surrounding air will end up with
different temperatures, even if they started out the same. The difference in
temperature leads to positive or negative buoyancy
for the air parcel.