Lithium is one of the main materials of fuel carrier salt in molten salt reactors. Its neutron cross section provides an important basic datum for physical design of molten salt reactor core and for evaluating the safety of the core during operation. The total neutron cross sections of natural lithium samples with thickness values of 8.00 mm and 15.0 mm are measured, respectively, in an energy range from 0.4 eV to 20 MeV by using a neutron total cross section spectrometer (NTOX) with the transmission method at the Back-n white neutron source of China Spallation Neutron Source (CSNS Back-n) with a 76.0 m time-of-flight path. High quality experimental data are obtained, especially in the energy region of keV and below, which supply a significative supplement of the data, thereby providing more abundant and reliable experimental data for nuclear data evaluation of lithium. Additionally, a theoretical analysis is carried out under the guidance of 1/v law and the multilevel R-matrix theory. And the resonance parameters of n+^6,7Li reaction around the energy of 260 keV are extracted from the measured data.