The motion of a light particle in an eccentrically rotating cylinder provides a method for verifying stationary history lift force effects at low but non-zero particle Reynolds numbers. We examine the flow in detail using a Lagrangian equation of motion for constant, non-zero-vorticity flows, and we predict a measurable and stationary contribution of history lift effects that can be verified experimentally with current experimental techniques. Because the history lift contribution is relevant only under certain conditions (which are determined in this work), the present flow configuration also allows one to isolate history drag effects under normal gravitation conditions without resorting to the tethered-particle arrangement used in previous works. We formulate and solve the trajectory problem for light particles that attain stable orbital motion, and we propose an experimental concept that makes possible the study of individual contributions of Lagrangian forces to the motion of small particles in viscous flows.