We discuss the implementation and characterization of our high-bandwidth arbitrary lattice generator. The periods and phases of multiple simultaneous 1D lattices can be modulated, swept and jumped at MHz rates to produce both arbitrary time-averaged potentials and dressed-band Hamiltonians. A Mach-Zehnder interferometer spans the dynamic range of the lattice allowing its complete characterization and stabilization in-situ. We demonstrate both disordered and dressed band Hamiltonians.