At least in the idealized, restricted three-body problem — two large bodies in circular orbit plus a satellite of negligible mass — the Lagrange points are true

At least in the idealized, restricted three-body problem — two large bodies in circular orbit plus a satellite of negligible mass — the Lagrange points are true points, but they represent not a destination for the satellite, but rather the center around which a near enough satellite will orbit harmonically, under essentially the same equations that govern a spring (a restorative force linear with displacement). It truly is a stable equilibrium in that sense. No station-keeping is required. In practice there will be slight perturbations due to the presence of other bodies, but the ∆V requirements for station-keeping are minimal.