Does he eat eggs and/or milk or is he a vegan?
Lacto-ovo vegetarian food is very easy to find in almost every single restaurant at WDW. It's also very easy to get on the fly--if there's something you'd like or someone on the menu that could be easily be made meatless, just ask the chef at the restaurant. It's usually no problem. Have him take a look at the menus at
www.wdwig.com and start scoping what he might like to eat.
If he's a vegan, it's a bit tougher. There are a few vegan menu options (The Grand Floridian Cafe has an AMAZING veggie burger and the Columbia Harbor House has a hummus/broccoli slaw sandwich that may also be vegan.) Your best bet for table service will be to call ahead and make special arrangements. WDW chefs are very accomodating and will make amazing creations if just given a little notice. I would choose what restaurants you would like to eat at, then 1-2 weeks before your trip, call the restaurant and speak with the chef about what you'll need. Call back 24 hours before your meal to confirm, and then let them know when you check in at the podium that you have made arrangements for a special meal.
As for the dining plan, most of the lacto-ovo food is already on the menu, so it really would be no different. If you're getting special vegan foods, just let the chef know you're on the dining plan when you make your initial call. You can make arrangements for all 3 courses then. It shouldn't be charged/credited any differently.
Hope you have a great trip!