We have studied the dynamics of warm dense Li with near-elastic x-ray scattering. Li foils were heated and compressed using shock waves driven by 4-ns-long laser pulses. Separate 1-ns-long laser pulses were used to generate a bright source of 2.96 keV Cl Ly- alpha photons for x-ray scattering, and the spectrum of scattered photons was recorded at a scattering angle of 120 degrees using a highly oriented pyrolytic graphite crystal operated in the von Hamos geometry. A variable delay between the heater and backlighter laser beams measured the scattering time evolution. Comparison with radiation-hydrodynamics simulations shows that the plasma is highly coupled during the first several nanoseconds, then relaxes to a moderate coupling state at later times. Near-elastic scattering amplitudes have been successfully simulated using the screened one-component plasma model. Our main finding is that the near-elastic scattering amplitudes are quite sensitive to the mean ionization state Z[over ] and by extension to the choice of ionization model in the radiation-hydrodynamics simulations used to predict plasma properties within the shocked Li.