  Gravitational lensing information from the two and higher point statistics of
the CMB temperature and polarization fields are intrinsically correlated
because they are lensed by the same realization of structure between last
scattering and observation. Using an analytic model for lens sample covariance,
we show that there is one mode, separately measurable in the lensed CMB power
spectra and lensing reconstruction, that carries most of this correlation. Once
these measurements become lens sample variance dominated, this mode should
provide a useful consistency check between the observables that is largely free
of sampling and cosmological parameter errors. Violations of consistency could
indicate systematic errors in the data and lens reconstruction or new physics
at last scattering, any of which could bias cosmological inferences and
delensing for gravitational waves. A second mode provides a weaker consistency
check for a spatially flat universe. Our analysis isolates the additional
information supplied by lensing in a model independent manner but is also
useful for understanding and forecasting CMB cosmological parameter errors in
the extended $\Lambda$CDM parameter space of dark energy, curvature and massive
neutrinos. We introduce and test a simple but accurate forecasting technique
for this purpose that neither double counts lensing information nor neglects
lensing in the observables.
