The Lives of Dax
anthology was first published in 1999, shortly after DS9 ended. It was a trade paperback novel (with a cream-colored cover, incidentally). It was not until Avatar
a year and a half later that the major relaunch story got rolling. For the 10th anniversary of DS9, The Lives of Dax
was reprinted, with a new, gold cover that included the relaunch logo. It was at this point that the books in the relaunch began including LoD in the reading list in the inside cover, along with A Stitch in Time
which did not receive a reprint.
Memory Beta lists the relaunch books in print order, but goes by the 2002 reprint date for LoD. So in terms of print order it is the first book in the relaunch. It was just that it was not explicitly identified with the relaunch until the reprint was issued, which seems to be what the list on Memory Beta goes by. Indeed, the relaunch itself did not really exist at that point, although the Ezri story coda in LoD makes it clear that the publishers were planning to continue the DS9 storyline.
As has been mentioned, several of the stories in LoD are referenced at various points although the Audrid and Joran stories are the critical ones to the relaunch saga. I think it helps to read LoD first since the anthology is referenced as early as in Avatar
but you will not be lost if you don't read it first or even if you skip it altogether (not that you'd want to).