Liquid metal walls have the potential solve to first-wall problems for fusion reactors, such as heat load and erosion of dry walls, neutron damage and activation, and tritium inventory and breeding. In the near term, such walls can serve as the basis for schemes to stabilize magnetohydrodynamic (MHD) modes. Furthermore, the low recycling characteristics of lithium walls can be used for particle control. Liquid lithium experiments have already begun in the Current Drive eXperiment-Upgrade (CDX-U). Plasmas limited with a toroidally localized limiter have been investigated, and experiments with a fully toroidal lithium limiter are in progress. A liquid surface module (LSM) has been proposed for the National Spherical Torus Experiment (NSTX). In this larger ST, plasma currents are in excess of 1 MA and a typical discharge radius is about 68 cm. The primary motivation for the LSM is particle control, and options for mounting it on the horizontal midplane or in the divertor region are under consideration. A key consideration is the magnitude of the eddy currents at the location of a liquid lithium surface. During plasma start up and disruptions, the force due to such currents and the magnetic field can force a conducting liquid off of the surface behind it. The Tokamak Simulation Code (TSC) has been used to estimate the magnitude of this effect. This program is a two dimensional, time dependent, free boundary simulation code that solves the MHD equations for an axisymmetric toroidal plasma. From calculations that match actual ST equilibria, the eddy current densities can be determined at the locations of the liquid lithium. Initial results have shown that the effects could be significant, and ways of explicitly treating toroidally local structures are under investigation.