IFMIF-DONES (International Fusion Materials Irradiation Facility- DEMO Oriented NEutron Source) is an installation aimed to irradiate with a high neutron flux materials relevant for the construction of the DEMOnstration fusion power plant (DEMO), in order to study the damage due to irradiation. Neutrons are generated using a 40 MeV and 125 mA deuteron beam impinging on a thick liquid lithium target. With these characteristics, damage due to irradiation comparable to those in the first wall of a fusion power reactor are achieved. In this paper we investigate the differences in the neutronic calculations of the IFMIF-DONES design when using different nuclear data libraries. We have first studied the differences in the neutron production due to Li(d,xn) reactions between different models and evaluations, comparing the different results with experimental data. Additionally, we have tested the performance of the MCNP6.2 and Geant4 Monte Carlo codes when using deuteron incident data libraries. Then, we have performed neutronic calculations of the IFMIF-DONES design using the most reliable Li(d,xn) neutron production models available, which are the FZK-2005 and the JENDL/DEU-2020 evaluations according to the results obtained in the first part of the study. Thus, the differences in these evaluations are propagated to different neutronic calculation results: neutron flux, primary displacement damage, gas production and heating in the materials to be irradiated. Finally, we have also carried out these same neutronic calculations, but using different nuclear data libraries for the neutron transport.