Bring the water, sugar, and salt to a boil in a small saucepan over medium-high heat, stirring until the sugar is dissolved. Reduce the heat and simmer for 3 minutes. Remove from the heat and cool to room temperature. Transfer the syrup to a small bowl and refrigerate, tightly covered until thoroughly chilled.
Whisk coconut milk and lychee juice in a large glass bowl. Whisk in the chilled syrup. Pour the mixture into an ice-cream maker and freeze according to the manufacturer's instructions. Transfer to a freezer container and freeze for at least 2 hours before serving.