This manuscript describes the design work and the R&D activities carried out for the third-generation neutron production target in the neutron Time-Of-Flight (n_TOF) facility at the European Laboratory for Particle Physics (CERN). The facility is composed of a neutron source coupled to two flight paths delivering a white-spectrum, pulsed neutron beam to two experimental areas. The neutrons are produced by the spallation reaction induced in lead-based target by a pulsed high-intensity proton beam with a momentum of 20 GeV/c extracted by the Proton Synchrotron, one of the circular particle accelerators of the CERN complex. The impact of high-energy proton beam pulses induces severe thermo-mechanical loads on the target, posing challenges for the target design. A description of the design process is provided, which started with the examination of multiple potential target concepts by means of numerical codes aimed to find a design offering an optimal combination of physics performance and thermo-mechanical response. The process converges towards a final design based on a series of pure-lead blocks supported by an anticreep structure in aluminum alloy and cooled by nitrogen gas. Novel approaches to simulate material response are presented and degraded operational scenarios are analyzed. The execution of two beam irradiation tests on target prototypes in a dedicated CERN facility is described, followed by post-irradiation examinations including neutron tomography inspections. The manuscript ends presenting the results of cyclic mechanical characterization tests on pure lead at different temperatures and strain-rates, and the proposal of a new constitutive model to better simulate the evolution of the material behaviour when subjected to repeated impacts of proton beam pulses.