True, I did not form a clear question, but I think stability analysis and stationkeeping control theory, for an actual mission, may require an understanding of the perturbations to a higher order than merely saying that to first order the telescope describes an ellipse with L2 at the center. Some halo orbits will be more stable than others, some of the perturbations can be worked out analytically, etc. Is that right? Wrong? Are they being so conservative with the orbit that a first-order analysis is enough?
First order is where we are at at the moment in explaining and understanding these orbits.
It is not where they are at when they actually calculate the necessary burns to keep it in its proper orbit.
The Moon is going to be the biggest influence, but also the easiest to correct for, being pretty regular.
Other planets, especially Jupiter, are going to exert an ever changing influence on it, and they will burn a bunch of CPU cycles on determining what those influences are, and correcting for them.
But it will always describe an ellipse with L2 just on the outside of the plane of that ellipse. over time, the L2 point will become further and further from the plane of the ellipse, and then they will do a burn to correct for that.
The longer they wait, and the further out the L2 point is, the more fuel needs to be burned, and the less efficient that burn is, reducing the service life.
I do wonder, when it comes time for the craft to be getting down to fumes, if they will use the fuel to keep it at L2 until the end, or if they will allow it to drift and use that fuel to maintain orientation instead, extending the life of the mission, though putting the telescope into a less and less useful position, being further and further from Earth.