In evolutionary biomechanics it is often considered that gaits should evolve to minimise the energetic cost of travelling a given distance. In gait simulation this goal often leads to convincing gait generation. However, as the musculoskeletal models used get increasingly sophisticated, it becomes apparent that such a single goal can lead to extremely unrealistic gait patterns. In this paper we explore the effects of requiring adequate lateral stability and show how this both increases energetic cost and the realism of the generated walking gait in a high biofidelity chimpanzee musculoskeletal model. We also explore the effects of changing the footfall sequences in the simulation so it mimics both the diagonal sequence walking gaits that primates typically use and also the lateral sequence walking gaits that are much more widespread among mammals. It is apparent that adding a lateral stability criterion has an important effect on the footfall phase relationship suggesting that lateral stability may be one of the key drivers behind the observed footfall sequences in quadrupedal gaits. The observation that single optimisation goals are no longer adequate for generating gait in current models has important implications for the use of biomimetic virtual robots to predict the locomotor patterns in fossil animals.