One of the main goals of the Large Hadron Collider (LHC) physics programme at CERN is to discover physics beyond the Standard Model (SM). A possible sign would be the observation of lepton flavour violation (LFV) that could be realised in decays of the Higgs boson or of the Z boson to pairs of leptons with different flavours.

I will present the result of a mutual search for the two LFV Z decays, Z⟶τe and Z⟶τμ, in the leptonic tau decay mode which exploits the fully data-driven eμ/μe-asymmetry method to estimate the SM background. The results will be compared to other analysis methods and experiments. I will also discuss possible applications of the eμ/μe-asymmetry method to other analyses, and its potential implementation in theoretical model-free searches.