We used coupling of flow and geometric confinement to assemble emulsion droplets in two-dimensional gliding lattices with a high degree of order and symmetry. Highly monodisperse discoid droplets with circular shapes were generated in a microfluidic flow-focusing device. Originally, close-packed lattices formed from these circular discoid droplets. Progressive confinement led to the gradual deformation of the circular disks: first, they elongated in the direction parallel to the direction of flow and then transformed into hexagons. Assembly driven by the combination of flow and confinement also allowed for the formation of lattices from droplets with a bimodal size distribution. We used photopolymerization of the monomer droplets to trap the lattice structure in the solid state and produce highly periodic arrays of solid polymer disks.