(1) Background: Postural sway is frequently used to quantify human postural control, balance, injury, and neurological deficits. However, there is considerably less research investigating the value of the metric in horses. Much of the existing equine postural sway research uses force or pressure plates to examine the centre of pressure, inferring change at the centre of mass (COM). This study looks at the inverse, using an inertial measurement unit (IMU) on the withers to investigate change at the COM, exploring the potential of postural sway evaluation in the applied domain. (2) Methods: The lipopolysaccharide model was used to induce transient bilateral lameness in seven equines. Horses were monitored intermittently by a withers fixed IMU over seven days. (3) Results: There was a significant effect of time on total protein, carpal circumference, and white blood cell count in the horses, indicating the presence of, and recovery from, inflammation. There was a greater amplitude of displacement in the craniocaudal (CC) versus the mediolateral (ML) direction. A significant difference was observed in the amplitude of displacement in the ML direction between 4–12 h and 168 h.; (4) Conclusions: The significant reduction in ML displacement during the acute inflammation period alongside greater overall CC displacement may be a compensatory behaviour for bilateral lameness.