From the often fascinating blog of mathematician John D. Cook, When do two-body systems have stable Lagrange Points?
[TL;DR: When the two main bodies have a mass ratio greater than 25:1. So: Sol/Earth yes, Earth/Luna yes, Pluto/Charon nope.]
[TL;DR: When the two main bodies have a mass ratio greater than 25:1. So: Sol/Earth yes, Earth/Luna yes, Pluto/Charon nope.]