To illustrate the advances made in permeability calculations combining X-ray microtomography and lattice Boltzmann method simulations, a sample suite of different types of pumices was investigated. Large three-dimensional images at high spatial resolution were collected at three different synchrotron facilities (Elettra, SLS, and ESRF). Single phase gas flow simulations were done on computer clusters with a highly parallelized lattice Boltzmann code, named Palabos. Permeability measurements obtained by gas flow simulation were compared to lab measurements of pumices produced by the Kos Plateau Tuff eruption to validate the method. New permeability data for pumices from other silicic volcanic deposits is presented, and an empirical model for permeability is tested using geometrical and topological data, i.e., tortuosity, specific surface area, and total and connected porosity.