We describe a highly robust method, applicable to both electromagnetic and matter-wave beams, that can produce a beam consisting of a lattice of orbital angular momentum (OAM) states coupled to a two-level system. We also define efficient protocols for controlling and manipulating the lattice characteristics. These protocols are applied in an experimental realization of a lattice of optical spin-orbit beams. The novel passive devices we demonstrate here are also a natural alternative to existing methods for producing single-axis OAM and spin-orbit beams. Our techniques provide new tools for investigations of chiral and topological materials with light and particle beams.