We use a Riordan group method to prove that certain classes of Riordan matrices count higher-dimensional lattice walks in Z^d that are of length n ending at height k. As a consequence of the method, unified lattice walk interpretations are given for certain sequences of matrices. Catalan-related solutions and first moments are computed and the average heights of the higher-dimensional walks are derived. Asymptotic estimates and lattice walk bijections are also given.