Intellectual exorcise, then.
Green Lanterns are fairly tough. Flight, any conceivable weapon at their command, crazy willpower, and they can just call in backup because they're space cops.
Mental attacks probably aren't a good idea, at least directly. Willpower is their whole thing. What I'd do is subject the Lantern to a series of emotional and psychological torments over the course of months or years, slowly whittling down their will to go on and any friends they can rely on, never letting on that I'm the one behind it all.
When they're at their weakest, BAM! I hit them out of nowhere and don't let up until they're down.
Hey son, wanna' learn how ta' make witch balls?