What can a lunar-based telescope do? If the band is ultraviolet and it can do high time sampling exposure, maybe it can be used to get distance for a star with stable pulses. However, the star should be bright and its distance should not be large.
What can a lunar-based telescope do?
First, you would have no atmospheric distortions to interfere with the viewing.
Second, there would be no atmospheric absorption of ultraviolet or infrared light.
Third, there would be no cloud cover, so viewing can be almost continuous (the sun may interfere).
However, the star should be bright and its distance should not be large.
I don't know what you reason for saying that, but it is unimportant since the Hubble telescope looks at all the stars.
The telescope will need to be self cleaning. There is a lot of dust kicked up when as meteoroid strikes.
An extended manned mission to the moon to set up a large array.