Lateralization is mostly analyzed for single traits, but seldom for two or more traits while performing a given task (e.g. object manipulation). We examined lateralization in eye use and in body motion that co-occur during avoidance behaviour of the common chameleon, Chamaeleo chameleon. A chameleon facing a moving threat smoothly repositions its body on the side of its perch distal to the threat, to minimize its visual exposure. We previously demonstrated that during the response (i) eye use and body motion were, each, lateralized at the tested group level (N = 26), (ii) in body motion, we observed two similar-sized sub-groups, one exhibiting a greater reduction in body exposure to threat approaching from the left and one--to threat approaching from the right (left- and right-biased subgroups), (iii) the left-biased sub-group exhibited weak lateralization of body exposure under binocular threat viewing and none under monocular viewing while the right-biased sub-group exhibited strong lateralization under both monocular and binocular threat viewing. In avoidance, how is eye use related to body motion at the entire group and at the sub-group levels? We demonstrate that (i) in the left-biased sub-group, eye use is not lateralized, (ii) in the right-biased sub-group, eye use is lateralized under binocular, but not monocular viewing of the threat, (iii) the dominance of the right-biased sub-group determines the lateralization of the entire group tested. We conclude that in chameleons, patterns of lateralization of visual function and body motion are inter-related at a subtle level. Presently, the patterns cannot be compared with humans' or related to the unique visual system of chameleons, with highly independent eye movements, complete optic nerve decussation and relatively few inter-hemispheric commissures. We present a model to explain the possible inter-hemispheric differences in dominance in chameleons' visual control of body motion during avoidance.