During operation, different diffusive and mechanical phenomena take place inside LIBs that result in a loss of performance and, eventually, threaten battery life. One of the main drawbacks affecting anode materials is the significant volumetric expansion (contraction) experienced by active material particles during lithiation (delithiation) processes, which may cause fracture. In this work, we present a novel numerical model to analyze coupled diffusion-mechanical problems accounting for material inhomogeneities. We are able to describe the nucleation of cracks and their propagation during particle cycling, depending on charging and discharging rates. Moreover, our model is able to reproduce complex fracture processes such as branching and change of directions. This description relies on combined use of a randomness parameter and a stochastic characterization of material properties within a lattice model approach. The model is used to analyze the effect of particle coating as a strategy to diminish the effect of transient cracking (that leads to early capacity fade). This is studied in detail at the coating-substrate interface and novel material designs are tested within our simulation framework.