Beam nuclei accelerated at the Large Hadron Collider (LHC) at CERN are lost due to interactions with the counter-rotating beam, residual gas, and accelerator elements. Proper modelling of the beam transport and radiation load on accelerator components requires reliable prediction of the yields of nuclear fragments produced in electromagnetic dissociation and hadronic fragmentation of beam nuclei. We investigate electromagnetic and hadronic fragmentation of lead nuclei in collisions with various nuclei and single electrons at the injection and collision energies of the LHC. The consideration is based on the RELDIS and abrasion-ablation models. Since this approach well describes Pb fragmentation data at 30 and 158 A GeV, its validity for Pb nuclei at the LHC collision energy is also expected.