In a small saucepan, combine sugar and water. Heat over medium heat until the sugar is completely dissolved, then simmer for 2–3 minutes. Remove from heat and let cool completely.

Open the refrigerated coconut milk cans and scoop out the thick coconut cream, discarding the liquid. Allow the cream to sit at room temperature for 15–20 minutes if very hard.

In a blender, combine coconut cream, cooled lemon syrup, lemon juice, lemon zest, and salt. Add vodka or rum if using. Blend until smooth and creamy.

Taste and adjust sweetness or tartness as needed by adding more lemon syrup or sugar.

Pour the mixture into a freezer-safe container, cover tightly, and freeze until solid, at least 4–6 hours or preferably overnight.

If frozen in a single container, remove and let soften for 5–10 minutes, then scoop into glasses. If frozen in ice cube trays, blend cubes with a splash of coconut milk until smooth.

Garnish with lemon slices or toasted coconut flakes before serving.