Loose-ring oil lift is a passive lubrication method widely used in self-contained bearing systems, but its application to heavy-duty pumps is limited by dynamic instabilities that compromise reliability. This study introduces a time-dependent numerical framework that, for the first time, captures the in-plane dynamic behaviour of oil rings. The governing equations of motion are newly derived from Lagrangian mechanics and solved using a fourth-order Runge–Kutta scheme. Forces acting on the ring are dynamically evaluated and coupled to ring motion, enabling accurate simulation of transient phenomena such as start-up and shut-down responses, perturbations, runout, and hysteresis effects. The solver is verified and validated against published computational and experimental data. Results reveal mechanisms underlying ring speed, lubricant transport, and attitude variations, providing a predictive tool for assessing stability and supporting the design of more reliable, cost-effective lubrication systems.