Ground-based detectors shine laser light from one mirror to another, allowing it to reflect back and forth hundreds of times in order to build up the effect of the gravitational wave on the light. But the LISA spacecraft are too far apart to use reflections.
So instead each spacecraft carries lasers. When light from one arrives at another, the on-board laser of the receiving spacecraft amplify the incoming light and return it, exactly as if it had been reflected, but much stronger. These “active mirrors” have never been used in spacecraft before. They have been demonstrated in the laboratory and are awaiting a test in space.