Gravitational flatness, the topography of Lagrange "points"

Just how gravitationally flat are real Lagrange Points? Many classic "jump drives" require "flat space" in order to fire, the classic diagram of Lagrange Points as shown below suggests ridges or plateaus of flat space with null gravity around the Lagrange Points but it deals with a simple three body system, solar systems are a good deal more complex so how much of that flatness is lost to perturbations from the likes of Jupiter, in other words influences outside the basic three body system of the Sun-Earth-Moon?

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Gravitational flatness, the topography of Lagrange "points"

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