Who does the Throw in?

[RookieDude]

A few officials got together last night and had a debate about who does a throw-in on a sideline in front court.

Trail on opposite side of Lead in front court. Lead has a ball go OOB on his line above the free throw line extended.

Does the Lead step up to administer the Throw in, thus causing a switch, or does the Trail go over to administer the Throw in, even though it was the Lead's line?

I've done it both ways...depending on how we pre-game it.
Would like to know the correct procedure, if there is one, so as not to get marked down in the post season.

Also, I usually have the Lead bounce pass to a player from the endline if the ball is OOB, frontcourt, on the sideline below the free throw line extended.

Dude