How does LISA get positions for its sources?
LISA’s response is not very directional, but its orbital motion around the Sun results in a modulation of long-lived signals in both amplitude and phase as the LISA “antenna pattern” of sensitivity sweeps across the position of the source. This modulation can help determine sky position, typically to about one degree. Another way to look at this is that during a year LISA establishes an observational baseline of two astronomical units (the Earth-to-Sun distance).