Working in batches if necessary, combine watermelon and sugar in work bowl of a food processor and process until smooth, about 1 minute. Pour purée through a strainer into an airtight container; you should have 1 quart of strained purée. Stir in and lemon juice to taste, 1 teaspoon at a time (see note). Stir in alcohol, then salt to taste, just enough to bring out natural flavor of the watermelon, and transfer to refrigerator to chill until very cold, 2 to 3 hours.
Churn in ice cream maker according to manufacturer's instructions. Optional: In last minute of churning, add cocoa nibs. Transfer to airtight container and chill for 2 to 3 hours in freezer until firm. Let sit on counter 10 minutes before serving to soften.
