Assuming gravity propagates at the speed of light as a force, rather than being an artifact of space-time, which would mean you don't get any waves. Which we've so far not been able to detect, probably because they don't exist. 8-).
Except for still having to explain the orbital decay of complex objects matching predictions based on GR involving loss of energy due to gravity waves and gravity traveling at the speed of light.
And you don't need a tetrahedron of space craft, just three space craft to confirm or deny the quadrupole nature of gravity waves.
It's a fun gedanken experiment, but I'm not sure the Lisa Pathfinder will be successful; the quadrupole formula requires that the plane of polarization be distinct, and that the orbit be an ellipse. The Lisa experiment has some fundamental assumptions about a collision being the wave source, rather than an orbital source.
It'd totally be a bummer to spend all that money and not see anything because the detector happens to be in a 2D plane coinciding with a detectable event, and the lack of additional planes made it invisible.
Personally, I have to believe that we have a fundamental misunderstanding of something, because we otherwise should have seen them in one of our existing detectors, if they were there to be seen. I don't think the longer baseline Lisa gives us is going to help detect something that we are fundamentally getting wrong somehow.
I used to joke with some of my friends that there's be two great reasons Michelson-Morely might not have shown anything:
(1) The reference frame is sufficiently pinned by the gravity well of the Earth that we don't see any drift through the "luminiferous aether" because we are frame-dragging at a higher degree than the equipment is capable of distinguishing.
(2) The Earth *really is the center of the Universe*, so also: no drift relative to the universe's inertial frame.
It may be that we won't see gravity waves (if any exist) until we get a device pretty far out into interstellar space.