A variant of the finite-difference time-domain (FDTD) algorithm - the Lebedev FDTD method - is augmented to allow for the simulation of electromagnetic waves in general dispersive anisotropic materials. Distinct dispersions may be applied to each of the principal axes of the anisotropic medium. The method is based on the auxiliary differential equation (ADE) and is simple to implement. Because of the collocated nature of the algorithm, multiterm dispersions necessary in previous implementations are avoided. Lebedev grid has previously been studied in detail by different research groups for simulation of anisotropy. In this work, we specifically focus on extending frequency dispersive materials to this method, and provide multiple examples to demonstrate the accuracy, validity and stability of the method.