The adiabatic lapse rate is a property of gases to cool as they drop in pressure. To the extent that pressure drops as altitude increases, atmospheric gases cool as they gain altitude. "Adiabatic" means no heat being added or taken away using any external source. Thus, the change in temperature represents the amount of work that the gases do on the surrounding gases. The work done is the integral of the change in the product of the pressure and the specific volume of the gas.
To the extent that greenhouse gases tend to be heavier than air, and thus bring up the specific gravity of air, they cause the pressure gradient to be very slightly steeper. Thus, the adiabatic lapse rate increases extremely slightly as CO2 concentration increases, and decreases extremely slightly when CH4 concentration increases.
MW Air = 29
MW CO2 = 44
MW CH4 = 16
Edit:
If you want to ask about the environmental lapse rate, and how greenhouse gases affect it, then the answer depends on the model used. http://en.wikipedia.org/wiki/Climate_models
1) The older models predicted a hot spot in the mid troposphere at 6 km up. In other words, it was expected that this altitude would heat faster than the surface, and faster than the zone above it. http://www.worldclimatereport.com/index.php/2004/07/19/the-data-weigh-in/
That never happened proving that there was something wrong with the original models. http://www.ssmi.com/msu/msu_data_description.html#msu_amsu_time_series
2) Like good scientists, they reworked their models which no longer predicts a hot spot at that altitude in the same sense as the old models. Now, 6 Km is the pivot point. The surface would warm the fastest. The amount of warming expected would decrease as the 6 km altitude is approached. At about 6 Km, the effect will be about neutral, and above 6 Km the atmosphere would cool. http://www.realclimate.org/index.php/archives/2004/12/why-does-the-stratosphere-cool-when-the-troposphere-warms/
The idea is that greenhouse gases capture heat closer to the surface, and convert it to wavelengths that the atmosphere is transparent to. Thus, in theory, the heat tends to have escaped and is no longer being trapped as we ascend in altitude beyond the 6 Km altitude.
All this means that in theory one would expect a greater lapse rate due to a greater temperature drop as one ascends in altitude.
Of course, this is partly an example of curve fitting after the original models that attempted to demonstrate CO2 as the primary cause of global warming failed. That explains the new agreement with the altitude data.