In a fully connected traffic environment with automated vehicles, new traffic control strategies could replace traditional traffic signals at intersections. In recent years, several studies about reservation-based intersection control strategies have been published, and a significant increase in capacity was shown. In the strategies presented so far, other road users usually play a minor role or are not considered at all. However, many use cases of automated driving occur in urban environments, where pedestrians and bicyclists play a major role. In this paper, a novel strategy for integrating pedestrians into automated intersection management is introduced and compared with a fully actuated traffic (AT) signal control. The presented control consists of a first-come, first-served strategy for vehicles in combination with an on-demand traffic signal for pedestrians. The proposed intersection control is explained, implemented, and tested on a four-leg intersection with several lanes coming from each direction. It dynamically assigns vehicles to lanes, and vehicles follow a protocol that enables cooperative lane-changing on the approach to the intersection. Demand-responsive pedestrian phases are included in such a way that predefined maximum pedestrian waiting times are not exceeded. A set of demand scenarios is simulated using a microsimulation platform. The evaluation shows that the presented control performs significantly better than the AT control when considering low, medium, and high traffic demand. Pedestrian waiting times are slightly improved and at the same time vehicle delays are substantially decreased. However, the control needs to be improved for scenarios with a very high vehicle demand.