This is doable. Greek appetizers are usually pretty healthy, lemon egg soup or roasted eggplant dip are all possibles in moderation. Greek salads with feta are OK and you might consider chicken gyros (the lamb and chicken are lower in fat). Steer clear of the macaroni and beef dish...I can't remember the exact name. If this is really fancy, you may also have a fish option. The desserts...well....they are generally low fat but high sugar, typically with nuts and honey.
Greek food is my absolute favorite and we ate it a lot when we lived near Chicago. Unfortunately, Washington doesn't have any really good places, but sushi is good so make the best of what you get. Good luck. Hope you have a good time.