Add water, salt, brown sugar, soy sauce, lime juice, and crushed ginger to a bowl and mix together until the salt and sugar have dissolved.
Place tuna steaks in a large sealable bag and pour in the brine/marinade. Place the bag in the refrigerator for 1-2 hours.
Preheat your pellet grill to 250°F with mesquite or hickory pellets in the hopper.
Remove tuna from the bag and rinse under cold water then pat dry.
Rub olive oil all over the tuna steaks and season both sides with fresh cracked black pepper
Place tuna steaks directly on the grates and smoke until the internal temperature reaches 145 °F (about an hour)
Remove tuna from the smoker, squeeze fresh lemon juice over them, and serve immediately.