  We calculate cross sections for inclusive dijet photoproduction in
electron-nucleus scattering in the kinematics of the future EIC and the
possible LHeC, HE-LHeC, and the FCC using next-to-leading order (NLO)
perturbative QCD and nCTEQ15 and EPPS16 nuclear parton density functions
(nPDFs). We make predictions for distributions in the dijet average transverse
momentum ${\bar p}_T$, the average rapidity $\bar{\eta}$, the observed nuclear
momentum fraction $x_A^{\rm obs}$, and the observed photon momentum fraction
$x_{\gamma}^{\rm obs}$. Comparing the kinematic reaches of the four colliders,
we find that an increase of the collision energy from the EIC to the LHeC and
beyond extends the coverage in all four considered variables. Notably, the LHeC
and HE-LHeC will allow one to probe the dijet cross section down to $x_A^{\rm
obs} \sim 10^{-4}$ (down to $x_A^{\rm obs} \sim 10^{-5}$ at the FCC). The ratio
of the dijet cross sections on a nucleus and the proton,
$\sigma_A/(A\sigma_p)$, depends on $x_A^{\rm obs}$ in a similar way as the
ratio of gluon densities, $g_A(x_A,\mu^2)/[A g_p(x_A,\mu^2)]$, for which
current nPDFs predict a strong suppression due to nuclear shadowing in the
region $x_A^{\rm obs} < 0.01$. Dijet photoproduction at future lepton-nucleus
colliders can therefore be used to test this prediction and considerably reduce
the current uncertainties of nPDFs.
