Bring the sugar and water to a boil over medium-high heat, stirring occasionally until the sugar dissolves. Reduce the heat, and simmer 5 minutes. Remove from heat, and cool.
Process the watermelon in food processor until smooth. Pour the watermelon puree through a fine wire-mesh strainer into a bowl, discarding the pulp.
Combine the sugar syrup, watermelon juice, wine or grape juice, and lemon juice in a covered container. Let chill at least 4 hours, or overnight. Pour into the container of 1 gallon electric ice cream processor; process according to manufacturer's instructions. Serve immediately, or place into an airtight container and store in the freezer.