Put steak and onion slices in a 1-gal. resealable plastic bag and pour in marinade. Seal bag and marinate in refrigerator, turning occasionally, at least 4 hours and up to overnight. Remove steak and onions, reserving marinade.
Prepare a gas or charcoal grill for high heat (you can hold your hand 1 to 2 in. above grill level only 1 to 2 seconds). Arrange steak and onions on grill and baste with marinade; close lid if using gas. Cook steak and onions until they begin to brown, 4 to 5 minutes. Turn over, baste again, and close lid. Cook onions until browned on both sides and softened, 2 to 3 minutes more; remove and set aside. Continue to cook steak until done to your liking, 10 to 12 minutes total for medium-rare. Transfer steak to a rimmed board or a platter and let rest 3 to 5 minutes.
Thinly slice steak across the grain. Season to taste with salt and pepper. Serve topped with onion slices and garnished with celery leaves and lemon wedges.