Measurements of the response function of LaBr3(Ce) to 2.5MeV neutrons have been carried out at the Frascati Neutron Generator and at tokamak facilities with deuterium plasmas. The observed spectrum has been interpreted by means of a MCNP model. It is found that the main contributor to the measured response is neutron inelastic scattering on 79Br, 81Br and 139La. An extrapolation of the count rate response to 14MeV neutrons from deuterium-tritium plasmas is also presented. The results are of relevance for the design of gamma-ray diagnostics of fusion burning plasmas.