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1
Prepare an ice-water bath; set aside.
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2
Combine the grapes and the water in a medium saucepan.
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3
Cook over medium-high heat until the liquid begins to bubble and the grapes start releasing liquid, about 4 minutes.
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4
Reduce heat, and simmer until the juices are dark purple and the grapes begin to break apart, about 3 minutes.
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5
Pass the mixture through a food mill and then through a fine sieve into a large bowl set in the ice bath; stir frequently until completely cool.
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6
Stir in the simple syrup and lemon juice.
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7
Transfer the mixture to an ice-cream maker, and freeze according to manufacturers instructions.
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8
Transfer to an airtight container, and store in the freezer until ready to serve, up to 2 weeks.