NavList:

Back on August 8, the Wall Street Journal published an article entitled, "How to Tell Time on the Moon".  The article is behind a paywall, but the most relevant/interesting bits of it are short enough to quote.

You can’t just take the gold standard of timekeeping on Earth—known as Coordinated Universal Time, or UTC—and extend it to the moon....

The problem is [that] time is affected by gravity. If you placed clocks on the Earth and moon and started them at exactly the same time, after 24 Earth hours, a clock on the lunar surface would be ahead by at least 56 millionths of a second, or 56 microseconds.

A difference of just one microsecond could result in an error of more than a mile in the estimated position of an object using Global Positioning System technology on Earth. Compound that error by at least 56 times for every day of a lunar mission’s lifespan, and suddenly the idea of a rocket hurtling toward the moon at 25,000 mph and then needing to slow down to slot into a congested lunar orbit sounds precarious.

I was unaware of this issue until August...but if you do a search for Coordinated Lunar Time, you will see that people have been discussing this for a while now.