I wondered about this too. My hunch was that they might be able to use the (comparatively) small detectors on earth to help localize the direction, while using the massive scale of LISA to analyze the details of the waveforms.
They won't be able to do that. LISA will be able to pick up signals with frequencies that can't be detected using LIGO/VIRGO/etc. LISA will be the only detector. However with three arms, it might be possible to localize the signal somewhat.
You would have to add a laser to all satellites and add another one.
It probably makes the satellite design a lot more complex and i don't know enough about orbital mechanics but wouldn't be surprised if it would get a lot more complicated as well to fly a 3d formation through space.
Indeed, a 4-satellite orbit is probably not a stable one unlike the 3-satellite orbit proposed for LISA. But the 4th satellite already isn't needed due to the conical orbit of the 3-satellite constellation. Fig 5(c) in "On the antenna pattern of an orbiting interferometer" [1] shows the antenna pattern for a LISA-like constellation and it's practically isotropic over a year, and for shorter periods the signals in LISA's sensitive band will be observed for long enough that they will not occupy its less sensitive directions for long and can thus still easily be detected with high SNR.
I can imagine how all of it adds up but still, it's way less than doing it again in 3D in who know in how many years. But maybe you are all right, it's too much for start.
to be fair, i can't imagine that an international group of very smart people with all sorts of PhDs sat around for however many years developing a plan after discussion after discussion would have their idea "bettered" by some rando on the internet. it's just fun to think about and wonder
