That would surprise me. As massive bodies are "wells" in spacetime, the LaGrange points would be mountain peaks - an unstable location for masses to be. However, the solar system's LaGrange points will move as the planets orbit, so a smart massive body can "surf" the downside slope of the moving peak.
The point is that they are indeed "wells." If they drift in slowly and aren't too massive, they'll stay. It takes energy to move them out.
(I'll admit to being unfamiliar with exactly what Lagrange calculated. But if he were wrong, we'd have noticed by now. I believe the opposite has happened.)