This thesis presents a new method to measure tau lepton universality in W boson decays at the LHC. Ratios of ℓτ_had and eμ final states are compared in tt̄ and Z → τ⁺ τ⁻ decays, with ℓ representing either a muon or electron, and τ_had is a tau lepton which decays hadronically. The double-ratio cancels uncertainties from τ_had lepton identification, which can be large at hadron colliders, and enables a precision test of tau lepton universality at the level of ~ 1.5%. This method is applied to data collected by the ATLAS experiment during 2015-2018 data taking at √s = 13 TeV, and indicates that lepton universality can be tested with ATLAS data at a precision of 1.6%. However there still remain differences between the expected Z → τ⁺ τ⁻ yields of the nominal and systematic signal simulation samples. These differences need to be understood before a precise measurement of lepton universality can be performed. In addition, a calibration of the τ had lepton identification methods used by the ATLAS experiment during 2015-2018 data taking at √s = 13 TeV is presented. The efficiency of the τ_had identification is measured in both data and simulation, and the resulting differences between the efficiency measurements are used to correct the efficiency in simulation to the observations in data.