We have measured the cross section for neutron radiative capture by Li at thermal neutron energy as 45.4+3.0 mb. We have compared this value, and the available fast-neutron-capture cross-section data on Li, with directand valence-capture theory. The mechanism of direct capture involving simple neutron-orbital transitions within a potential well can adequately account for the magnitude of the thermal-neutron-capture cross sections and the shape of the fast-neutron-capture cross sections. We recommend that the capture cross sections from the theoretical calculation, instead of those from a recent measurement, be used for nuclear astrophysics calculations. If the fast-neutron-capture data are normalized at 25 keV to the theoretical value, the magnetic-dipole (M 1) radiation width of the 255-keV p-wave resonance can be deduced. It is in agreement with the value calculated from a valence theory for M1 capture, thus lending support for this neutron-capture mechanism as an important one, at least for light nuclei. We also find some evidence from our analysis of the total cross-section data for a possible energy dependence of the potential required to describe the almost pure single-particle s-wave resonances underlying the Li cross section.