In the framework of the Work Package Early Neutron Source (WPENS) of the EUROfusion Consortium, the engineering design of the IFMIF-DONES (International Fusion Material Irradiation Facility - Demo Oriented Neutron Source) lithium target system has been accomplished. The development of the design required that new neutronic calculations had to be performed in ENEA, in order to update those already achieved in the past for the previous geometrical layout. The aim of these evaluations is to provide quantities, such as power deposition, dpa and gas production, useful for the thermo-mechanical analysis that is required for assessing the structural behavior of the system subjected to irradiation. Coupled neutron-gamma transport calculations have been carried out by using the MCNP6.2 code integrated with the McDeLicious-17 neutron source. The geometrical input for MCNP used in the calculations was provided by KIT. Neutron activation calculations have been also performed by means of the FISPACT-II activation code package in order to provide radioactive quantities, such as decay heat and contact dose rates, in various parts of the system, useful for thermo-mechanical analysis and safety purposes, like waste management considerations. This paper presents the main results obtained from the above analyses.