1. Prepare an ice bath; set aside. Combine grapes and the water in a medium saucepan. Cook over medium-high heat until the liquid begins to bubble and grapes start releasing liquid, about 4 minutes. Reduce heat, and simmer until juices are dark purple and grapes begin to break apart, about 3 minutes.

2. Pass 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. Stir in simple syrup and lemon juice.

3. Transfer mixture to an ice-cream maker, and freeze according to manufacturer's instructions. Transfer to an airtight container, and store in the freezer until ready to serve, up to 2 weeks.