Fohn winds
The effect caused by a fohn is not due to any difference in density, though density will change. The point is that as the air cools as it rises it reaches the dew point (becomes saturated) and condensation occures. As it crosses the summit of the mountain it warms as it decends. However, because it has lost so much of its moisture on and below the summit the dew point of the air is lower, so the height at which the air becomes unsaturated is higher than it was on the windward side. From that point down the air warms at the unsaturated lapse rate, so the air at the foot of the mountain is warmer than it was on the other side of the hill, as well as being dryer.
For most calculations the Saturated Adiabatic Lapse Rate is 1.8 degrees per 1000 feet (0.6/300 m) - 1.98 degrees per 1000 feet is the ISA environmental lapse rate.