We analyse lithium sputtering, evaporation and transport for the National Spherical Torus Experiment (NSTX) liquid lithium divertor (LLD) for planned high heating power plasma conditions. A temperature-dependent, data-calibrated, surface-response model is used to specify sputter yield, velocity distributions, sputtered Li ion fraction and related phenomena, for the static liquid lithium surface with D, Li and trace C impingement. Using the surface-response model, and supplied UEDGE code edge plasma parameters and LLD surface temperature profile for a typical 2 MW heating, low D-recycle shot, the REDEP/WBC code package computes Li erosion/redeposition. The results are encouraging showing negligible Li evaporation, moderate sputter erosion, and acceptable Li transport to the edge (∼7% Li/D density) and core plasma (∼1% Li/D contamination potential) and LLD adjacent surfaces. A 2% carbon plasma content does not significantly affect the LLD surface response. For fixed plasma conditions, but with hypothetically higher surface temperatures than the reference 281 °C peak, an increase to ∼350 °C appears acceptable, thus implying a significant operating temperature margin.