|Cellular automata are discrete dynamical systems with locally defined behaviour, well known as simple models of complex systems. Classically, their dynamics derive from synchronously iterated rules over finite or infinite configurations; however, since for many natural systems to be modelled, asynchrony seems more plausible, asynchronous iteration of the rules has gained a considerable attention in recent years. One question in this context is how changing the update schedule of rule applications affects the global behaviour of the system. In particular, previous works addressed the notion of maximum sensitivity to changes in the update schemes for finite lattices. Here, we extend the notion to infinite lattices, and classify elementary cellular automata space according to such a property.