It may help in understanding the mechanic if you consider
Why the Lead would cross over,
What they then officiate, and therefore
Where they will be positioned. This was the major focus of the camp I went to this summer, so let me relate their philosophy.
The purpose of crossing over is to officiate the low post when on the side opposite of where the Lead is primarily working. Without crossing over, the Lead will be straight-lined on the play. So you cross the lane and position yourself within a step of the lane, looking back into the key. Now you are positioned perfect to look between the low post and the defensive player. In this position you
do not pick up responsibility for the portion on the court near the end line on the side that both officials are now standing. (And the Trail
does not cross over to the other side.) The Lead's responsibility is still the other side, which is the direction you're facing.
The point is on a defensive rebound, you are no more than one step from the paint anyway, so crossing back to your side as you progress down the court as
Trail is not a problem. Just don't get caught in the middle and close to the action if there is a steal, and the play is now running right over you.
