NASA blasts a 1000Watt laser at the moon on a regular basis, in fact the Goddard center has an even bigger one going in place to give them a better return pulse for range finding. Yes they actually measure how far away the moon is quite a bit
Lasers lose power on a logarithmic scale, so to hit the moon with enough power of a laser beam to actually heat the ground, not destroy anything, but act as a space heater, the ground based laser here would have to be so big that the atmosphere would boil, and they would have to use most of the power that the United states generate to fire the beam. Attenuation from our atmosphere is huge, but the distance is just mindbogglingly large.
So if you did have a moon base, you have about 5000 years before technology is at a point where someone can shoot a laser at your base from earth and even be noticed on the moon.