Bring 3 c water to boil in a heavy large pot. Stir in barley, lentils, and rice. Reduce heat to low. Cover and cook until grains are tender, about 40 minutes. Transfer to large bowl. Drain; cool.
Heat 1/4 c oil in a heavy large skillet over medium-low heat. Add carrots, onion, celery, sunflower seeds, and garlic and saute until vegetables are tender, about 12 minutes. Add to grains and cool. Mix in basil, thyme, and oregano. Season with salt and pepper. (Can be made 1 day ahead. Cover and refrigerate.)
Preheat oven to 300F. cut tops off pita rounds to form pockets. Wrap in foil an place in oven to warm.
Stir beaten eggs and flour into grain mixture. Press 1/2 c mixture between palms of hands to form patty. Repeat with remaining mixture. Heat film of oil in heavy nonstick skillet over medium-high heat. Add patties in batches and cook until golden brown and heated through, about 5 minutes per side.
Place 1 patty in each pita round. Top with lettuce and tomatoes and serve.