Google's Pregel vertex-centric programming model has led to a class of component-centric abstractions that are widely used for designing and executing distributed graph algorithms in a Bulk Synchronous Parallel (BSP) manner on commodity clusters. There has, however, been little effort to formally understand the behavior of such programming models to allow analytical comparison of graph algorithms with narrow bounds. Graphs and graph algorithms have asymmetry that make them challenging to model effectively. Lattice (or grid) graphs, commonly used in scientific computing, offer a simpler structure to tackle this novel problem. Here, we propose analytical models with tight bounds on the coordination, computation and communication costs for performing a vertex-centric Breadth First Search (BFS) on uniform lattice graphs. We validate these further with empirical results. Our results hold for lattice graphs of arbitrary dimension and uniform odd-valued length, but can be extended to non-uniform lengths as well. These results offer a formal understanding of the behavior of vertex-centric BFS for a lattice structure, and lays the foundation for further analysis and exploration of component-centric algorithms.