  In this letter we analyze the associated production of a vector meson with
the bound - free $e^+e^-$ process in ultraperipheral $PbPb$ collisions through
the double scattering mechanism for the energy of the Large Hadron Collider
(LHC). Such process is characterized by the presence of a meson and a positron
in the final state and by a forward hydrogen - like ion with a distinct
electric charge. We present our predictions for the total cross sections and
rapidity distributions considering the rapidity ranges covered by the ALICE and
LHCb detectors, which indicate that a future experimental analysis of the $\phi
+ e^+$ and $J/\Psi + e^+$ final states is feasible.
