In principle, Kinetic Lattice Monte Carlo (KLMC) methods can accurately simulate the precipitation of coherent phases by tracking the motion of a vacancy and the corresponding diffusion and clustering of solutes. The fidelity of the KLMC simulations depends primarily on the validity of the assumed interatomic potentials. These potentials must provide accurate solute-solute-solvent-vacancy energetics over the length scales relevant to the physical decomposition paths. Of course, simulating long range strain energy interactions is the biggest challenge, but the significance of this contribution is less in systems manifesting primarily dilational strains. Simple nearest neighbor (NN) potentials, used in previous KLMC of decomposition kinetics of dilute Fe-Cu alloys are generally not able to reproduce alloy property combinations like vacancy formation energies, dilute heats of solution and the coherent interface energies. Further, solute diffusion in bcc alloys requires jumps between first and second nearest neighbors, and is governed by, at minimum, at least three independent jump frequencies. The jump frequencies are controlled by the binding energies of atoms out to at least second nearest neighbor positions (which are only about 15% further away from the solute than the first nearest neighbor) and are also influenced by solute-modified saddle point activation energies. Thus longer range multiatom embedded-atom-method (EAM) type potentials can, in principle, provide a more realistic simulation of diffusion and solute clustering compared to NN based models. However, this refinement comes at a much higher computational cost. While they cannot be directly compared, this study presents KLMC results for both a simplified EAM versus a NN potential, and describes important new mechanistic insight provided by these atomistic simulations.