This is not about creating a time zone, but a time standard. That 58-ish microseconds per day relativistic difference in time is the entire reason for the project. UTC is based on International Atomic Time, which is an average reading of hundreds of atomic clocks placed around the surface of the Earth. LTC will have to be based on the readings of atomic clocks on the surface of the Moon in order to establish a consensus standard in that relativistic frame of reference. For practical reasons, the system will also have to keep track of offsets from UTC so that any given timestamp could be converted between UTC and LTC in a standardized way. The same principle could be applied to other planets and moons if needed.
As noted in the Celestial Time Standardization memo, having a time standard that is accurate to your frame of reference is useful if you want to have something like GPS navigation, or to calibrate instruments that rely on the definition of the SI second, e.g. a laser range finder:
