Getting industrial grade lasers is the easy part.. it seems to be within range of aliexpress available tattoo removal laser (based on the laser pulse energies listed in https://en.wikipedia.org/wiki/Lunar_Laser_Ranging_experiment... and rough laser tattoo removal energies listed in https://pmc.ncbi.nlm.nih.gov/articles/PMC10421900/ .. take aliexpress rating with grain of salt)

You do need access to a large telescope (at least 1.2m based on the wiki article), a sensitive detector (is photomultiplier tube sensitive enough??) and most importantly, access to your local laser clearinghouse so you don't accidentally shoot an airplane, blind the pilot and got arrested, or a satellite and start a war (if you believe some guy on quora). Probably the last part is the hardest thing for an amateur