We report on the scaling between the lift force and the velocity lag experienced by a single particle of different size in a monodisperse dense granular chute flow. The similarity of this scaling to the Saffman lift force in (micro-) fluids, suggests an inertial origin for the lift force responsible for segregation of (isolated, large) intruders in dense granular flows. We also observe an anisotropic pressure field surrounding the particle, which potentially lies at the origin of the velocity lag. These findings are relevant for modeling and theoretical predictions of particle-size segregation. At the same time, the suggested interplay between polydispersity and inertial effects in dense granular flows with stress and strain gradients, implies striking new parallels between fluids, suspensions, and granular flows with wide application perspectives.