Preheat oven to 350 degrees. Combine gingersnap crumbs and melted butter in medium bowl; stir until blended. Press mixture along bottom and sides of 13-x9-x2-inch baking dish. Bake for 10 minutes.
Combine rice, milk, and sweetened condensed milk in a 2-quart saucepan. Cook over medium heat until thick and creamy (approx. 20 to 25 minutes), stirring frequently. Remove from heat and stir in lime juice. Pour filling into prepared crust; chill.
Spread whipped cream over pudding. Cut into bars and garnish with lime peel, if desired.