A model to predict the scatter on fatigue response of a "generic" material based on knowledge of the statistical variations of microstructural parameters is proposed. The model is based on Discrete Damage Mechanics (DDM), whereby microstructural elements are considered individually via a two-dimensional Delaunay lattice and its conjugate Voronoi tessellation. The elements of the lattice are modeled as truss elements with a linear elastic response and a normal distribution of static strengths. These elements represent boundaries between domains, which can be individual grains. Damage is constrained to intergranular cracking to simplify the simulation. A Baquin-type law is assumed to describe the fatigue behavior of each element and fatigue damage is accumulated via a Palmgren-Miner law. The fatigue behavior is assumed the same for all elements to study the effects of geometrical disorder and load redistributions on the macroscopic response. The lattices were cycled under strain control for 9 values of strain amplitude with zero mean strain. One hundred replicas with different local geometries were used to obtain statistics at each strain level. Results indicate that the geometrical disorder combined with load redistribution results in significant scatter in fatigue life. Further analysis indicated that the cycles to failure followed an exponential distribution at high cycles, but a lognormal distribution provided a better overall fit when low cycles were included. The macroscopic response followed a Coffin-Manson behavior, where the exponent of the power-law was essentially the same as the one used to represent the fatigue behavior of the individual elements, This indicates that lattice models can replicate the behavior observed experimentally in structural materials, while providing the advantage of making it possible to study variations in microstructural properties and geometry separately. Discussion on how to extend and calibrate the proposed model to actual material is offered.