  The dilepton production in diffractive and exclusive processes at forward
rapidities considering ultraperipheral $PbPb$ collisions at the LHC is
investigated. Predictions for the $e^+ e^-$, $\mu^+ \mu^-$ and $\tau^+ \tau^-$
cross sections are presented taking into account of realistic cuts that can be
implemented by the LHCb Collaboration in a future experimental analysis. Our
results indicate that the background associated with the diffractive production
can be strongly suppressed and the exclusive processes can be cleanly
separated. For the $\tau^+ \tau^-$ production, the semi and purely leptonic
decay channels are considered. Our results indicate that a future experimental
analysis of the dilepton production at the LHCb is feasible and can be useful
to search for BSM physics.
