ESA has expressed interest in establishing a standard for timekeeping on the Moon, in particular for artificial satellites to be deployed around the Moon.

https://www.esa.int/Applications/Navigation/Telling_time_on_the_Moon

One solution would be to simply reference everything to Earth UTC time, but there may be technical reasons to prefer an independent Moon standard. From the article:

“…[C]locks on the Moon run faster than their terrestrial equivalents – gaining around 56 microseconds or millionths of a second per day. Their exact rate depends on their position on the Moon, ticking differently on the lunar surface than from orbit…”