We study the extent to which the lateral ocelli of dragonflies are able to resolve and map spatial information, following the recent finding that the median ocellus is adapted for spatial resolution around the horizon. Physiological optics are investigated by the hanging-drop technique and related to morphology as determined by sectioning and three-dimensional reconstruction. L-neuron morphology and physiology are investigated by intracellular electrophysiology, white noise analysis and iontophoretic dye injection. The lateral ocellar lens consists of a strongly curved outer surface, and two distinct inner surfaces that separate the retina into dorsal and ventral components. The focal plane lies within the dorsal retina but proximal to the ventral retina. Three identified L-neurons innervate the dorsal retina and extend the one-dimensional mapping arrangement of median ocellar L-neurons, with fields of view that are directed at the horizon. One further L-neuron innervates the ventral retina and is adapted for wide-field intensity summation. In both median and lateral ocelli, a distinct subclass of descending L-neuron carries multi-sensory information via graded and regenerative potentials. Dragonfly ocelli are adapted for high sensitivity as well as a modicum of resolution, especially in elevation, suggesting a role for attitude stabilisation by localization of the horizon.