1. Preheat oven to 425°. Fold 8 (16- x 12-inch) squares parchment paper in half crosswise; unfold and arrange parchment pieces on 2 baking sheets.
2. Evenly divide onion slices among parchment pieces; sprinkle each salmon fillet on both sides with a total of 1 tablespoon Greek seasoning. Place 1 fillet, skin side down, on top of onions near fold of each parchment piece; top each fillet with 3 lemon slices and 1 tablespoon butter. Fold top half of each parchment piece over fish, overlapping small folds along edges; seal. Brush each parchment packet with olive oil, and bake until parchment packets puff up (about 8-10 minutes).
3. Transfer parchment packets directly to plates or a work surface. Carefully cut tops of packets open, making sure to avoid hot steam. Sprinkle fish with salt and pepper to taste. Serve with couscous and fresh steamed or sautéed vegetables.