Excerpt from BBC article:

"The mission to demonstrate technologies needed to detect gravitational waves in space has been a stunning success.

The Lisa Pathfinder satellite was sent into orbit to test elements of the laser measurement system that would be used on a future observatory.

Performance objectives were exceeded on the very first day the equipment was switched on."

BBC Article

The European Space Agency (ESA) has a brief article on the science challenges and new technologies. see:

A perfectly still laboratory in space

As an aside, the orbits of the three satellites (two yet to be launched) will be at various Lagrange Points (L1, L2, L3, ... ) which are known to be flat space-time points. This makes the going easier, since tidal forces are minimized as well as minimizing any micro-gravity.

An explanation of the Lagrange Points, where these spacecraft will be sitting "on" in space-time, is given on the ESA site link:

What are Lagrange Points?

A diagram of several of these point is below. Notice that two bodies have 5 Lagrange Points. Below you can see the earth-Moon L1, L2, ..., L5 and also the Sun-Earth SEL1 and SEL2. The SEL3,...SEL5 are not shown.

 also, here is a photo showing the saddles, peaks and troughs with a fictional representation of space-time that is dramatically enlarged. The system shown below is the Lagrange Points for the Earth-Moon System.