The Lagging Tail makes the holder go last in its priority bracket. For example...
- A Zebstrika with Lagging Tail using Thunderbolt (0 priority) will go after a Riolu using Bite (0 priority).
- A Zebstrika with Lagging Tail using Quick Attack (+1 priority) will go before a Riolu using Bite (0 priority).
- A Zebstrika with Lagging Tail using Quick Attack (+1 priority) will go after a Riolu using Vacuum Wave (+1 priority).
It doesn't change a move's priority.
Lagging Tail (Bulbapedia)