We revisit the convergence of loop-erased random walk, LERW, to SLE2 when the curves are parametrized by capacity. We construct a Markovian coupling of the driving processes and Loewner chains for the chordal version of LERW and chordal SLE2 based on the Green's function for LERW as martingale observable and using an elementary discrete-time Loewner "difference" equation. We keep track of error terms and obtain power-law decay. This coupling is different than the ones previously considered in this context, e.g., in that each of the processes has the domain Markov property at mesoscopic capacity time increments, given the sigma algebra of the coupling. At the end of the paper we discuss in some detail a version of Skorokhod embedding. Our recent work on the convergence of LERW parametrized by length to SLE2 parameterized by Minkowski content uses specific features of the coupling constructed here.