What we could do is the following:
1. We can design a spaceship/spacecraft, like voyager
2. and send it into space with it's sole purpose to function as a reflector
for us.
Voyagers (and more modern interplanetary probes) use two way ranging
(or even three way ranging).
In this system, a well known data sequence is sent towards the probe
at an exactly known frequency. The interplanetary probe receives the
stream, performs an _exact_ fractional frequency change (say 1/2 or
240/221) and sends the data immediately back to Earth.
When the signal is received on Earth, the distance to the probe can be
calculated with a fraction of the wavelength (at least in principle).
Since the frequency change ratio is exactly known, the doppler shift
also gives a very accurate radial speed (regardless of probe local
oscillator stability). To get the tangential position and speed,
celestial mechanics can be used to reduce the possible solutions.
The frequency change at the probe is required, since if it would
transmit the response back on the same frequency, it would block the
receiver.
Anyway, this principle would make "active" mirrors on the lunar
surface feasible at giga or terabit speeds with somewhat sensible
power levels.
3. And then we can use it to keep sending laser beams at it.
This would still need some frequency shifting system on visible
wavelengths.
If the receiving and transmitting stations could be installed at
wildly separate locations on the Moon, receiving the signal from with
one telescope, amplify with erbium amplifiers, transfer it to some
location in an other crater with optical fiber and somehow amplify it
to kW level and send it back to Earth with an other telescope. Most
likely, the sending and receiving stations on Earth would also have to
be quite far from each other, possibly on different continents, in
order to avoid direct leakage from Tx to Rx.