Measuring a non-zero value for the cross section of any lepton number violating (LNV) process would put a strong lower limit on the washout factor for the effective lepton number density in the early universe at times close to the electroweak phase transition and thus would lead to important constraints on any high-scale model for the generation of the observed baryon asymmetry based on LNV. In particular, for leptogenesis models with masses of the right-handed neutrinos heavier than the mass scale observed at the LHC, the implied large washout factors would lead to a violation of the out-of-equilibrium condition and exponentially suppress the net lepton number produced in such leptogenesis models. We thus demonstrate that the observation of LNV processes at the LHC results in the falsification of high-scale leptogenesis models. However, no conclusions about the viability of leptogenesis models can be drawn from the non-observation of LNV processes.