  We discuss the associated $c\bar{c}$ and $l^+l^-$ pairs production in
ultraperipheral heavy-ion collisions at high energies. Such a channel provides
a novel probe for double-parton scattering (DPS) at small $x$ enabling one to
probe the photon density inside the nucleus. We have derived an analog of the
standard central $pp$ pocket formula and studied the kinematical dependence of
the effective cross section. Taking into account both elastic and non-elastic
contributions, we have shown predictions for the DPS $c\bar c l^+l^-$
production cross section differential in charm quark rapidity and dilepton
invariant mass and rapidity for LHC and a future collider.
