  We forecast how current ({\planck}) and future ({\prism}) cosmic microwave
background (CMB) experiments constrain the adiabatic mode and its admixtures
with primordial isocurvature modes, using measurements of the reconstructed CMB
lensing potential and lensing-induced CMB B-mode polarization anisotropies in
combination with the CMB temperature and E-mode polarization anisotropies. We
first study the characteristic features of the CMB temperature, polarization
and lensing spectra for adiabatic and isocurvature modes. We then consider how
lensing-induced B-mode polarization and lensing potential information can
improve constraints on an admixture of adiabatic and three correlated
isocurvature modes. We find that the CMB lensing spectrum improves constraints
on isocurvature modes by at most 10% for the {\planck} and {\prism}
experiments, with the limited improvement a result of the low amplitude of
isocurvature lensing spectra and cancellations between these spectra rendering
them only slightly detectable. There is a larger gain from using the
lensing-induced CMB B-mode polarization spectrum, as measured by {\prism}, with
constraints on isocurvature mode amplitudes improving by as much as 40%
relative to the CMB temperature and E-mode polarization constraints. The
addition of both lensing and lensing-induced B-mode polarization information
constrains isocurvature mode amplitudes at the few percent level or better,
with percent level constraints or better possible in the case of admixtures of
the adiabatic mode with one or two correlated isocurvature modes. We
investigate the dependence of our results to various assumptions in our
analysis, such as the inclusion of dark energy parameters, the CMB
temperature-lensing correlation, and the presence of primordial tensor modes,
and find that these assumptions do not significantly change our main results.
