I mostly agree with you. The three body problem (3+) is chaotic at those timescales. But I suppose all thats needed for predicting this lensing is a two body problem if they're isolated enough, which is much more predictable
Which just means there’s no closed form solution. You can simulate these bodies fine provided you have sufficient numerical accuracy and very accurate measurements of initial conditions (this is the part that’s practically impossible)
Take a Monte Carlo approach. Run a bunch of simulations to generate a probabilistic point cloud in spacetime of where the lenses end up. Fire a signal through every point in the cloud.
