The challenge of computing ionic transport coefficients from first principles is to achieve the necessary convergence with respect to system size, simulation time, and configurational sampling. Unfortunately current computer resources are not yet available for such convergence studies at the fully first principles level. In this work, a lattice kinetic Monte Carlo model is used to study the convergence properties of transport coefficients, using the Li sub-lattice of the Li ion electrolyte Li2OHCl as an example system. The specific transport coefficients representing tracer diffusion, effective diffusion, and mobility are carefully studied for their convergence properties. Additionally, ion pair correlations of the effective diffusion are recast as a sum over events which allows for a detailed study of the nature of the correlation in terms of time and spatial separation. This experience suggests a general method of performing simulations by using first a kinetic Monte Carlo model followed by a first principles molecular dynamics study. For the Li2OHCl system, the kinetic Monte Carlo results provide both a reference for the Haven ratio due to purely geometric effects and a measure of the computational effort needed to obtain meaningful molecular dynamics results. The combination of the two methods provides further evidence of anti-correlated Li-ion motion in this system as predicted in a previous study.