Wash swordfish well and make sure it is dry before putting on grill. Lightly salt.
Mix onions, parsley, olive oil, lemon juice, salt and pepper in a bowl.
Grill swordfish until firm to the touch (anywhere from 3-5 minutes on each side depending on thickness). Cook less if you enjoy your swordfish a bit rarer. Remove from grill and top with lemon parsley mixture. Serve immediately.