This study describes the charge‐state evolution of relativistic lead ions passing through a thin aluminum stripper foil. It is motivated by the Gamma Factory project at CERN, where optical laser pulses will be converted into intense gamma‐ray beams with energies up to a few hundred MeV, achieved via excitation of atomic transitions in few‐electron heavy‐ions at highly relativistic velocities. The recently developed BREIT code is employed together with theoretical cross‐sections for single‐electron loss and capture of the projectile ions. All charge‐states starting from Pb 54 + up to bare ions are considered at kinetic projectile energies of 4.2 and 5.9 GeV u −1 . During recent Gamma Factory beam tests, the calculated preparatory predictions allow to effectively produce Pb 80 + and Pb 81 + ions from Pb 54 + in the transfer beam line between the PS and SPS synchrotron accelerators at CERN and consequently, to store partially stripped ions in the LHC for the very first time. Reasonable agreement is found between the calculations and the very few experimental data available. The study lays the groundwork to optimize the yields of charge states of interest for experiments within the future Gamma Factory project, including the upcoming Gamma Factory Proof‐of‐Principle experiment for which predictions for the production of Pb 79 + are presented.