Previous Monte Carlo simulations of the distribution of adsorbates in zeolites have suggested that adsorbates are confined to a lattice of sites in the micropore. In this work, we examine the effect of the structure and energetics of the adsorption site lattice on the mobility of small molecules in cage-like micropores using Monte Carlo lattice dynamics (MCLD) simulations. In MCLD, motion is modeled as a series of activated site-to-site hops over energetic and entropic barriers whose magnitudes can be functions of zeolite structure, sorbate chemistry, and loading. The topology of the lattice is such that adsorbate hops are of two types : (i) between sites in a given cage, and (ii) between sites in neighboring cages. For comparison, an analytical model of adsorbate self-diffusivity is constructed by applying a random walk theory to this lattice. This model is exact at low loading and approximates the dynamics well even for a crowded lattice. We also compare MCLD to molecular dynamics (MD) simulations of methane adsorbed in zeolite A and observe qualitative agreement between the two approaches. However, the computational cost of MCLD is an order of magnitude lower than MD.