What a fluffy, fact-free article. They have studiously avoided any concrete assertions. So will this proposed Lunar Clock be tracking Earth time, or will it be independent, and based on the day/night cycles on the Moon itself?

Mars already has a system of Sols (days) that are independent of Earth time -- obviously, because Mars is nowhere near a range for instantaneous communications.

Elsewhere on HN, I believe I read that it would be impractical, or at least not cost-effective, to stand up a LPS (lunar positioning system) comparable to the Earth satellites.

I'm very surprised such a thing doesn't exist already. Maybe a good place to set it from would be Tranquility Base where Aldrin and Armstrong landed.