Recent experiments illustrate that the morphology of the electrode surface impacts the voltage - capacity curves and long term cycling performance of Li-ion batteries. The present study systematically explores the role of the electrode surface morphology and uncertainties in the reactions that occur during electrochemical cycling, by performing kinetic Monte Carlo (kMC) simulations using the lattice Boltzmann method (LBM). This allows encoding of the inherent stochasticity at discrete microscale reaction events over the deterministic mean field reaction dynamics that occur in Li-ion cells. The electrodes are taken to be dense thin films whose surfaces are patterned with conical, trapezoidal, dome-shaped, or pillar-shaped structures. It is shown that the inherent perturbations in the reactions together with the characteristics of the electrode surface configuration can significantly improve battery performance, mainly because patterned surfaces, as opposed to flat surfaces, result in a smaller voltage drop. The most efficient pattern was the trapezoidal, which is consistent with experimental evidence on Si patterned electrodes.