Andrew Sarangan wrote:

Instability produces cumulus clouds and stability produces stratus
clouds.

Better to say "can result in" rather than "produces". That's because in
addition to atmospheric lapse rate characteristics, moisture content of
the air also determines when and where clouds will form. Many stable
situations actually act to dissipate 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?

Almost. The formation of a cumulus cloud is already an indication that
some localized instability has occurred. After the cloud has formed, it
is more likelly to remain unstable because the air within it is
saturated, and will cool at a slower rate as it rises than will
unsaturated air. This is due to the latent heat released by additional
droplet formation as the cloud grows.

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?

It really is just what you said at the start of your paragraph: an
average lapse rate. Observed lapse rates will vary all over the map,
sometimes greater, sometimes less than the average. Sometimes lapse
rates can go negative, which results in an inversion (warm air over
cold). What they won't do is exceed the dry adiabatic rate (the
3C/1000' you mentioned). This is because instability will result, and
convective overturning will restore the lapse rate to dry adiabatic.

An excellent introductory text explaining these issues is "Atmospheric
Science, an Introductory Survey", by Wallace and Hobbs. It's written
for a 2nd semester atmospheric science student, but is very readable.

Jim Rosinski