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A new, more precise measurement of the Λ hyperon lifetime is performed using a large data sample of Pb−Pb collisions at sNN−−−√=5.02 TeV with ALICE. The Λ and Λ¯¯¯¯ hyperons are reconstructed at midrapidity using their two-body weak decay channel Λ→p+π− and Λ¯¯¯¯→p¯¯¯+π+. The measured value of the Λ lifetime is τΛ=[261.07±0.37 (stat.)±0.72 (syst.)] ps. The relative difference between the lifetime of Λ and Λ¯¯¯¯, which represents an important test of CPT invariance in the strangeness sector, is also measured. The obtained value (τΛ−τΛ¯¯¯¯)/τΛ=0.0013±0.0028 (stat.)±0.0021 (syst.) is consistent with zero within the uncertainties. Both measurements of the Λ hyperon lifetime and of the relative difference between τΛ and τΛ¯¯¯¯ are in agreement with the corresponding world averages of the Particle Data Group and about a factor of three more precise.