Measured and calculated neutron spectra from a sphere of lithium metal with natural isotopic composition are compared. In the calculations, the investigation is concentrated on the SN method with nuclear data from ENDF/B-III for lithium and from KEDAK 3 for iron. A special partition of the angular coordinate, S19, was introduced to allow for the strong anisotropy of the neutron flux in the radial direction. For the proper treatment of the anisotropic elastic scattering, a new technique for improved, extended, and consistent transport approximation up to T5 is used. These ameliorations being introduced, it is shown that the nonelastic scattering is treated inadequately with respect to the angular and energetic distribution of the outcoming neutrons. The investigation is completed by a comparison of the measured and calculated space-dependent tritium production rate, in which the discrepancy is found consistent with the discrepancy in the neutron spectra. Furthermore, we propose that the 7Li(n,n′α) cross section should be reduced by 15 to 20% with respect to the ENDF/B-III value.