The spacecraft have the job to prevent disturbances affecting the test masses. They are equipped with special low-thrust jets called FEEPS; these are fired to counter-act external forces on a spacecraft and ensure that it does not bump into the test masses. This is called drag-free control; it has been demonstrated in other missions, but never to the degree of isolation required by LISA.
Making sure that the spacecraft does not influence the motion of the test masses is a major requirement. Even small effects, like the changing gravitational influence of parts of the spacecraft on the proof mass as the spacecraft expands and contracts due to small fluctuations in the light from the Sun, may have important effects and must be controlled.