The viability of using liquid-lithium walls for the divertor and main chamber surfaces for a Fusion Nuclear Science Facility (FNSF) is analyzed from the point of view of the edge-plasma region that separates the hot core plasma from the surrounding material walls. The edge plasma is modeled by the UEDGE two-dimensional multifluid transport code that evolves equations for the density, momentum, and temperature of a 50%/50% mixture of deuterium-tritium (DT) ions, impurity ions, and electrons. Neutral DT and impurity gases are represented by neutral fluid equations. The primary inputs from the FNSF design are the magnetic configuration, plasma-facing-surface locations, core plasma exhaust power, and core boundary DT ion density. Lithium sources and sinks due to evaporation and condensation on the plasma-facing surfaces are parameters. The results show that a highly radiating divertor plasma, detached from the divertor plates, can be formed where >90% of the exhaust power is radiated by lithium with a broad deposition profile on plasma-facing surfaces that yields peak heat fluxes in the range of 2 MW/m2. The detached configuration is dominated by lithium plasma in the divertor and by hydrogen plasma upstream adjacent to the core boundary. A nonnegligible low level of lithium is found upstream at the outer midplane, typically in the range of 3% to 20%, that represents a potential core DT fuel dilution problem. An important physical mechanism is the collisional thermal force acting between ion species that can push impurities upstream along the magnetic field lines. Results show that the effect of reduced DT recycling at lithium surfaces due to hydride formation does not significantly affect the stability and radiative efficiency of the lithium divertor.