Yes. The Soviet Lunokhod program built and flew two successfully in the early 1970s. I don't know the details of how they did this, but it would make sense to use more automation today. A 2.6 second ping time is long enough that pilots who have played modern video games are likely to complain :).
I don't think ping is the problem... the problem is "line-of-sight"... Obviously, Earth rotates too fast, so you'd need to use a network of Earth-satellites getting the signal from the moon and transmitting it to the ground station. The other problem, maybe, is how to communicate... Can you have an antenna/laser on the rover itself, or would it need to transmit to a Moon-satellite first (e.g. to save weight on the lander)? How much energy do you need to communicate, can you do it continuously or do you need to "save" energy for a quick burst of radio signals every so often? Is there any other kind of interference (Moon regolith allegedly flies up to 100km above the surface)...
These are just simple issues that came to my mind. No idea how relevant they are, and if there are more relevant issues.
Yes. The Soviet Lunokhod program built and flew two successfully in the early 1970s. I don't know the details of how they did this, but it would make sense to use more automation today. A 2.6 second ping time is long enough that pilots who have played modern video games are likely to complain :).