You have mentioned that the dry adiabatic lapse rate was 5.4 degrees per thousand feet. While flying in the Navy, we used the figure 3.4 degrees, which usually was observed as the outside air temperature at altitude. Why the difference?
The difference is between dry and wet adiabatic lapse rates. The dry adiabatic lapse rate is the rate at which dry air cools as it rises (or warms as it descends): a loss of 5.4 degrees per thousand feet of ascent (or a gain of 5.4 degrees per thousand feet of descent). By “dry air,” we mean air in which water vapor has not condensed into visible water droplets. The figure that you give, 3.4 degrees per thousand feet, is rate of temperature change when water vapor has condensed into visible droplets, that is, in clouds or fog. It is the wet adiabatic lapse rate.