Lunge feat allows you to extend your reach by five feet. Can Lunge be used to extend the reach of a grapple attempt? Can it be used to extend the reach of a trip attempt? If either case is true, and the opponent does not have reach, is it even possible to take an attack of opportunity (if allowed) against the attacker?
You can't use Lunge with a grapple maneuver because initiating a grapple is a standard action (not usable as part of an attack action).
A trip attempt, instead, can replace a melee attack. In this case is not clear if it benefits from the same feats of a regular melee attack. If so, then Lunge can apply, but you still provoke an attack of opportunity unless you possess the Improved Trip feat.