An object in a planet's lagrange points is not a satellite of the planet (it isn't orbiting the planet); it would be a co-orbital instead.
Technically, it's gravitationally bound to both objects, and can be said (except for L3) to be a part of the "system" of both, but only orbiting body 1... (L3 being opposite body 1 from body 2).
L1 and L2 are in fact orbits of body 2 which happen also to be resonant with a matching orbit of body 1.
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