Grate 2 tablespoons lemon zest and reserve. Juice the lemons and reserve the juice separately. Place the lemon juice and the pineapple chunks in a blender and puree until smooth. Strain through a fine-mesh strainer into a large measuring cup. Add the reserved zest and stir together. You should have about 4 cups of puree. For each 4 cups of puree, measure 1 cup sugar.

Place approximately 1/4 of the puree in a saucepan. Add the sugar and stir over medium heat until the mixture is simmering and the sugar has melted. Add this to the remaining puree and stir together. Place in the refrigerator and chill until cold.

Freeze according to the instructions for your ice cream maker.