I was wondering this earlier and found this question, but it wasn’t the clearest. I THINK it’s saying that you’ll go last within your move’s priority bracket but I wasn’t entirely sure. Can someone confirm this?
Lagging Tail does indeed make you move last in your priority bracket. So, if both pokémon use a priority move, the pokémon with a Lagging Tail would move last, regardless of speed.
SOUrce: https://m.bulbapedia.bulbagarden.net/wiki/Lagging_Tail#:~:text=The Lagging Tail (Japanese: こうこうのしっぽ Second-Batter Tail) is,in Generation IV that delays the holder's turn.