In a small heavy bottomed saucepan over medium heat, add the pineapple, sugar, water or pineapple juice, lemon juice and zest. Stir just until sugar melts. Let cool to room temperature.

Transfer pineapple mixture to a food processor, with 1 cup buttermilk. Puree until smooth. With the motor running, gradually add remaining buttermilk, until smooth and well blended.

Pour into a freezer-safe dish and place in the freezer. Freeze until firm, at least 2 hours. Eat and enjoy!