Mark and Rocket have covered the subject pretty well...I can only add a little to what they have said.
Once we put the academic definition aside, the real question is one of what we use lag pursuit for. There is no single answer.
One purpose of lag pursuit (or 'flying in lag') is to take a high angle off/high aspect angle situation where you are in danger of overshooting the bandit. By going lag on the bandit, you gain the turning room needed to avoid the overshoot. An example of this is the High Yo-Yo.
Another purpose of lag pursuit is to reduce excessive closure in low angle off/aspect situations. Going lag extends your flight path and creates a reduction in closure through geometry and perhaps an actual reduction in airspeed as well. This is the Vector Roll.
Lastly, a common form of lag pursuit is for a BnZ fighter to ease off the turn when chasing a TnB target. By flying a faster but wider turn, the BnZ fighter is able to match the target's turn rate and retain a position of advantage. This is probably the most often thought of form of lag pursuit.
Back to academics for a moment. Any out-of-plane maneuver is, by definition, lag pursuit. Most texts define lag pursuit using in-plane examples...ie, nose on, nose in lag, nose in lead.
So, Spitlead, anytime in a turning dogfight, when you think you have too much closure or you think you have too much lead and may be in danger of overshooting the bandit, move your nose behind or out-of-plane (or both) to help remedy the situation.
Andy