This work describes a technique for forming nanometer-scale pixilated lipid domains that are self-organized into geometric patterns residing on a square lattice. In this process, a lipid multibilayer stack is deposited onto a silica substrate patterned with a square lattice array of bumps, hemispherical on their sides, formed by electron beam lithography. Domain patterns are shown to be confined to the flat grid between the bumps and composed of connected and individual domain pixels. Analysis of lattices of varying sizes shows that domain pattern formation is driven by mechanical energy minimization and packing constraints. We demonstrate single lattice sizes and a gradient in lattice size varying from the micrometer to the 100 nm scale applicable to precise arraying, patterning, and transport of biomolecules that partition to lipid domains.