The viability of thermal leptogenesis scenarios can be investigated model independently at the LHC. We show that once a non-zero cross section of a lepton number violating process is measured, a strong lower limit can be set on the washout factor for the effective lepton number density in the early universe at times close to the electroweak phase transition. We further demonstrate that this in turn leads to severe constraints on high-scale models for the generation of the observed baryon asymmetry based on lepton number violation. Especially for right-handed neutrinos heavier than the mass scale at which lepton number violation is observed at the LHC, the resulting washout factor will reduce any pre-existing lepton asymmetry exponentially, rendering leptogenesis ineffective.