Nope, a single Lighthouse transmitter can give full position -- at some accuracy. If you use multiple photodiodes (receivers) with a known rigid-body transformation between them, you can infer the receiver unit's full 6-DoF pose.
For example, you could (naively) estimate distance using two photodiodes if you knew that they were separated by 5cm. If the difference in measured angles is small, they're far away. If it's large, then they're near. (The full 6-DoF situation is a little more complex, but the same idea.)
> It can actually (poorly) track a moving object with just one sensor and one base station...
We didn't expect this at all, it is not immediately intuitive, but even 2D simulations display this behavior. If you can tell me why, really why, you should apply for a job at Valve. :)
(Apparently 5 sensor hits are required for a proper fix.)
For example, you could (naively) estimate distance using two photodiodes if you knew that they were separated by 5cm. If the difference in measured angles is small, they're far away. If it's large, then they're near. (The full 6-DoF situation is a little more complex, but the same idea.)