Place salt and fish in a large zip-top plastic bag; shake bag to coat fish evenly. Chill 8 hours or overnight.
Remove fish from bag; rinse well. Soak fish in ice water 2 hours, changing water every 30 minutes. Drain well. Pat fish dry with paper towels. Dice fish; place in a large bowl. Set aside.
Soak white onion in ice water 15 minutes. Drain well. Add diced onion, green onions, and diced tomato to fish; toss gently to combine. Spoon about 3 tablespoons fish mixture into each lettuce leaf.