In small bowl mix oil lemon juice and OLD BAY. Place tuna steaks in large resealable plastic bag and add marinade. Turn to coat well.
Marinate in fridge 20 minutes (longer for extra flavor).
Transfer fish to grill and discard leftover marinade. Broil or grill over medium heat 5 to 6 minutes per side or until desired doneness. (Tuna is more moist when its center is still rosy-pink after cooking.)