My answer to Does the distance to L2 vary? is
The correct answer is "No, they are only mathematically defined when the orbit is circular".
but @DavidHammen's answer explains that they can be defined in the elliptical restricted three body problem and @PM2Ring's answer shows that JLP's Horizons provides eight specifically defined Lagrange points from which you can calculate distances to other things; L1, L2, L4 and L5 for the Earth/Moon system and for the Sun/Earth-Moon-Barycenter system.
Question: How (the heck) does JPL define the exact position of Lagrange points in the real solar system where (I thought that) they can't be defined?
There must be some kind of compromise here as Horizons reflects a realistic n-body simulation without any "restricted three body" conditions that I know of. They must use some equation or rule to calculate the position of these spots that I don't believe can be defined. What is it?