Whisk first 3 ingredients in a 2-quart pitcher or large bowl until blended. Cover and chill 30 minutes. Whisk coconut milk, lemon juice, and salt into milk mixture.
Pour milk mixture into freezer container of a 1-quart electric ice-cream maker, and freeze according to manufacturer's instructions. (Instructions and times will vary.)
Remove container with ice cream from ice-cream maker, and place in freezer 15 minutes. Transfer to an airtight container; freeze until firm, about 1 to 1 1/2 hours. Serve ice cream with toasted coconut, shaved chocolate, or chopped macadamia nuts.
Note: For testing purposes only, we used a Rival 4-quart Durable Plastic Bucket Ice Cream Maker and a Cuisinart Automatic Frozen Yogurt-Ice Cream & Sorbet Maker.
Note: To make a tropical sundae, top coconut ice cream with sliced bananas, mango slices, and pineapple chunks.