(written from a Production point of view)
The term ADR looping is used in the film making industry as an abbreviation for automated dialogue replacement or additional dialogue recording. It is the technical name for "looping", the process of re-recording dialogue following photography.
As an in-joke for an okudagram made for "Up The Long Ladder", "ADR looping" was listed as the mission of the SS Seattle, under the command of Wendy Neuss that departed from Earth in 2120. The mission type was replaced for the remastered version of the episode with a diplomatic mission to SR-47 instead.