The neutron time-of-flight (n_TOF) facility at the European Laboratory for Particle Physics (CERN) is a pulsed white-spectrum neutron spallation source producing neutrons for two experimental areas: the Experimental Area 1 (EAR1), located 185 m horizontally from the target, and the Experimental Area 2 (EAR2), located 20 m above the target. The target, based on pure lead, is impacted by a high-intensity 20-GeV/c pulsed proton beam. The facility was conceived to study neutron-nucleus interactions for neutron kinetic energies between a few meV to several GeV, with applications of interest for nuclear astrophysics, nuclear technology, and medical research. After the second-generation target reached the end of its lifetime, the facility underwent a major upgrade during CERN's Long Shutdown 2 (LS2, 2019-2021), which included the installation of the new third-generation neutron target. The first- and second-generation targets were based on water-cooled massive lead blocks and were designed focusing on EAR1, since EAR2 was built later. The new target is cooled by nitrogen gas to avoid erosion-corrosion and contamination of cooling water with radioactive lead spallation products. Moreover, the new design is optimized also for the vertical flight path and EAR2. This paper presents an overview of the target design focused on both physics and thermomechanical performance, and includes a description of the nitrogen cooling circuit and radiation protection studies.