Twisted photonic lattices that form moiré superlattices have attracted significant attention owing to their unique properties, in which the localized optical modes can serve as efficient light sources. However, in conventional moiré lattices, the emission direction of confined modes is typically fixed, and achieving a broad range of emission angles remains a significant challenge. Here, we design and fabricate single-layer moiré photonic lattices into cylindrical geometries using a nanomembrane origami technique. This approach enables wide-angle localized-mode emission while maintaining stable single-mode operation and excellent spectral uniformity. The moiré supercells support localized flat-band modes under various effective twist angles, resulting in the observation of periodic localized-mode emission over a wide range of azimuthal angles. Our research provides an approach for developing moiré light sources on curved surfaces, offering significant potential in applications that demand spatial light control, including three-dimensional imaging, light detection and ranging, and topological state manipulation.