Bring water and sugar to a boil in a large sauce pan; add lemon juice and gelatin mix. Stir until dissolved and set aside to cool.
Transfer cooled gelatin mixture to a 5-quart container and stir in pineapple juice. Freeze until thickened but not solid, about 2 hours.
Spoon about half the pineapple-lime mixture into a large punch bowl. Top with 1 bottle lemon-lime soda. Refill with remaining frozen mixture and soda as needed.