  We analyze the ability of galaxy and CMB lensing surveys to constrain massive
neutrinos and new models of dark radiation. We present a Fisher forecast
analysis for neutrino mass constraints with the LSST galaxy survey and the CMB
S4 survey. A joint analysis of the three galaxy and shear 2-point functions,
along with key systematics parameters and Planck priors, constrains the
neutrino masses to $\sum m_\nu = 0.041\,$eV at 1-$\sigma$ level, comparable to
constraints expected from Stage 4 CMB lensing. If low redshift information from
upcoming spectroscopic surveys like DESI is included, the constraint becomes
$\sum m_\nu = 0.032\,$eV. These constraints are derived having marginalized
over the number of relativistic species ($N_{\rm eff}$), which is somewhat
degenerate with the neutrino mass. We also explore the gain by combining LSST
and CMB S4, that is, using the five relevant auto- and cross-correlations of
the two datasets. We conclude that advances in modeling the nonlinear regime
and the measurements of other parameters are required to ensure a neutrino mass
detection. Using the same datasets, we explore the ability of LSST-era surveys
to test "nonstandard" models with dark radiation. We find that if evidence for
dark radiation is found from $N_{\rm eff}$ measurements, the mass of the dark
radiation candidate can be measured at a 1-$\sigma$ level of $0.162\,$eV for
fermionic dark radiation, and $0.137\,$eV for bosonic dark radiation, for
$\Delta N_{\rm eff} = 0.15$. We also find that the NNaturalness model of
Arkani-Hamed et al 2016, with extra light degrees of freedom, has a sub-percent
effect on the power spectrum: even more ambitious surveys than the ones
considered here will be needed to test such models.
