International Fusion Materials Irradiation Facility-DEMO Oriented NEutron Source (IFMIF-DONES) 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 that in the first wall of a fusion power reactor is achieved. In this paper we investigate the differences in the neutronic calculations of the IFMIF-DONES design when using different nuclear data libraries. We first studied the differences in neutron production due to Li(d, xn) reactions between different models and evaluations, comparing the different results with experimental data. Additionally, we tested the performance of the MCNP6.2 and Geant4 Monte Carlo codes when using deuteron incident data libraries. Then, we 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 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 also carried out these same neutronic calculations while using different nuclear data libraries for the neutron transport