The electromagnetic production of a dilepton pair in the muon-ion scattering, usually denoted muon trident process, is investigated considering the feasibility of studying processes induced by muons at LHC using its far-forward detectors. The total and differential cross-sections are estimated taking into account of the Bethe-Heitler and bremsstrahlung channels, and predictions for the event rates expected for muon-tungsten ( μW ) collisions at the LHC energies are presented. Our results indicat