The n_TOF facility, a spallation neutron source, uses a pure lead target to produce neutrons with a 20-GeV proton beam extracted from the CERN Proton Synchrotron. After 4 yr of operation and [approximately]3 yr of cooling, the present spallation target is damaged and was moved to its provisional storage place in the n_TOF service gallery and will be later transferred to a Swiss repository. In this study, to deal with the removal and storage of the lead target, detailed isotope production and residual dose rate calculations were performed with the FLUKA Monte Carlo code. The study further includes a detailed analysis of three-dimensional residual dose rate fields around the target and through the installation pit. It addresses critical design parameters for the new target and successfully compares the simulation results to recently available measurement data. FLUKA allows residual dose rates to be calculated using two different approaches: a one-step approach that simultaneously takes into account production and decay (built-in) and a two-step approach that allows for flexible geometries between the isotope production and sampling of the decay products (customized). This work shows the clear advantage of performing Monte Carlo calculations prior to interventions and waste disposal and the importance of a detailed description of all the installation components, a complete chemical composition inventory, and a correct irradiation profile.