We discuss lepton flavour violating processes induced in the production and decay of heavy right-handed neutrinos at the LHC. Such particles appear in left-right symmetrical extensions of the Standard Model as the messengers of neutrino mass generation, and can have masses at the TeV scale. We determine the expected sensitivity on the right-handed neutrino mixing matrix, as well as on the right-handed gauge boson and heavy neutrino masses. By comparing the sensitivity of the LHC with that of searches for low energy LFV processes, we identify favourable areas of the parameter space to explore the complementarity between LFV at low and high energies.