Air temperature changes with elevation

I am curious about how relative humidity affects the moist adiabatic lapse rate.

Using the lapse rate equation, I calculated that as humidity decreases, the lapse rate should increase, since the value of e, the water vapour pressure of the saturated air, decreases. (thus affecting r, the mixing ratio of the mass of water vapour to the mass of dry air)

Am I right that as humidity decreases, MALR increases (thus temperature change is greater)?