Within the framework of an extensive programme devoted to the search for alternative candidates for the neutrino mass determination, the atomic mass difference between ²⁰²Pb and ²⁰²Tl has been measured with the Penning trap mass spectrometer ISOLTRAP at the ISOLDE facility at CERN. The obtained value Q_EC= 38. 8 (43) keV is three times more precise than the AME2012 value. While it will probably not lead to a replacement of ¹⁶³Ho in modern experiments on the determination of the electron-neutrino mass, the electron capture in ²⁰²Pb would however allow a determination of the electron-neutrino mass on the few-eV level using a cryogenic micro-calorimeter.