The surface-assisted hierarchical self-assembly of DNA origami lattices represents a versatile and straightforward method for the organization of functional nanoscale objects such as proteins and nanoparticles. Here, we demonstrate that controlling the binding and exchange of different monovalent and divalent cation species at the DNA-mica interface enables the self-assembly of highly ordered DNA origami lattices on mica surfaces. The development of lattice quality and order is quantified by a detailed topological analysis of high-speed atomic force microscopy (HS-AFM) images. We find that lattice formation and quality strongly depend on the monovalent cation species. Na⁺ is more effective than Li⁺ and K⁺ in facilitating the assembly of high-quality DNA origami lattices, because it is replacing the divalent cations at their binding sites in the DNA backbone more efficiently. With regard to divalent cations, Ca²⁺ can be displaced more easily from the backbone phosphates than Mg²⁺ and is thus superior in guiding lattice assembly. By independently adjusting incubation time, DNA origami concentration, and cation species, we thus obtain a highly ordered DNA origami lattice with an unprecedented normalized correlation length of 8.2. Beyond the correlation length, we use computer vision algorithms to compute the time course of different topological observables that, overall, demonstrate that replacing MgCl₂ by CaCl₂ enables the synthesis of DNA origami lattices with drastically increased lattice order.