Combine water and sugar in a saucepan. Bring to a boil; stir to dissolve sugar. Remove from heat; add lemon zest. Let cool to room temperature, about 15 minutes.
Stir pineapple, pineapple juice, and lemon juice into sugar mixture.
Beat egg whites in a bowl using an electric mixer until stiff. Fold egg whites into sugar-juice mixture.
Pour mixture into a glass baking dish; place in freezer. Stir thoroughly every half hour; chop through ice as it forms and incorporate egg whites. Continue until frozen to desired consistency, 2 to 4 hours.