In a small saucepan combine water, sugar, and corn syrup. Bring just to boiling, stirring to dissolve sugar; remove from heat. Cool to room temperature.
In a food processor or blender combine 1/2 of the fruits and 1/2 of the pineapple juice; cover and process or blend until smooth. Transfer to a shallow 3-quart freezer-safe container or dish. Repeat with remaining fruit and juice; add to dish. Stir in the cooled syrup and the lemon juice.
Cover and freeze until just firm, about 4 to 5 hours. For a fluffier texture, break up mixture and transfer to a chilled large mixing bowl; beat until fluffy, but not melted. Return to freezer container, spreading evenly. Freeze until firm.
Let stand 10 minutes at room temperature before scooping to serve. Makes 8 servings.