The growth of renewable energies, together with their power converter interfaces, reshapes power systems into more-electronics power systems. Along with this paradigm shift is the requirement of grid formation by grid-tied power converters. However, existing grid architectures only allow parallel operation of grid-forming converters, which excludes high-voltage applications. This article proposes novel lattice power grids that combine the advantages of multilevel converters and power grids, thereby allowing both serial and parallel connectivity with modularity and scalability. Further, we propose control and optimization algorithms for lattice power grids by use of graph theory. In particular, we investigate H-bridge-based lattice power grids and achieve several objectives, including desired voltages and currents between any two selective nodes in lattice power grids as well as efficiency optimization by minimizing switching actions. To achieve these objectives, this article details control and optimization methodology for square lattice power grids. Finally, the proposed algorithms and lattice power grids are validated via simulation results.