Atmospheric stability and lapse rate

Instability produces cumulus clouds and stability produces stratus clouds.
We know that. However, since the saturated and unsaturated lapse rates are
significantly different (1C/1000' compared to 3C/1000'), it seems quite
possible to get cumulus clouds even when the atmosphere below is stable.
For instance, if the environmental lapse rate is 2C/1000', the unsaturated
air is stable. Once clouds form (how they form without vertical currents is
a different matter), the air inside the clouds will become unstable. Does
this seem reasonable?

On a related question, where does the concept of 'average' lapse rate
(2C/1000') come from? I always took this to mean 50% RH air, but it took me
a long time to learn that that was not the case. The air is saturated or it
is unsaturated. How can there be an average between saturated and
unsaturated? The standard lapse rate and standard temperature at
different elevations are all based on this 2C/1000' concept. What's the
deal with this?