Although there is no solution for the general three body problem there are many related results, especially for the restricted case.  <a href="https://arxiv.org/abs/1106.5062"> Here is a study of LE's</a> in restricted 3BP.  <a href="https://arxiv.org/abs/1205.0950">And here is a classification scheme</a> for the mean motion resonance of the restricted 3BP including using the maximal LE for characterizing the resonances.  These will point you to many related results.  As a historical aside, Gutzwiller, in his book[1] says that the ancient Greeks knew there were 3 different lunar months (depending on how you measure them in they sky): the Sidereal month (27.32166 days), the anomalistic month (27.55455 days) and the nodical month (27.21222 days).  These result from 3 body interactions (earth, moon, sun).  The Greeks were apparently able to observe these to an accuracy of 1 second per month.  Gutzwiller calls these the first precision scientific measurements in history.  Every time I think about this I am astonished; it must have taken immense effort over centuries to compile the needed data.

[1] Martin C. Gutzwiller <a href="https://www.amazon.com/Classical-Quantum-Mechanics-Interdisciplinary-Mathematics/dp/0387971734">Chaos in Classical and Quantum systems.</a>