Prepare the brine by mixing kosher salt, brown sugar, and lemon juice in water. Use a bowl or lsealable, eakproof bag.
Place tuna steaks in the brine and refrigerate for 3 hours. There's no need to soak overnight due to tuna's quick absorption.
Preheat the smoker to 200°F with mild wood chips like fruit wood; avoid intense woods like mesquite, which overpowers tuna's mild taste.
After brining, remove the tuna steaks from the bag and place them on the smoker rack for even smoke circulation.
Cook until the tuna steak reaches an internal temperature of 140°F (about 60 minutes); avoid overcooking to retain flavor. You can serve once done as there's no need for resting.